STRUCTURAL HYBRIDIZATION AND ECONOMICAL OPTIMIZATION OF STRENGTHENING SYSTEMS USED

FOR CONCRETE BEAMS

MD. MOSHIUR RAHMAN

FACULTY OF ENGINEERING UNIVERSITY OF MALAYA

KUALA LUMPUR

2016

STRUCTURAL HYBRIDIZATION AND

ECONOMICAL OPTIMIZATION OF

STRENGTHENING SYSTEMS USED FOR

CONCRETE BEAMS

MD. MOSHIUR RAHMAN

THESIS SUBMITTED IN FULFILMENT OF THE

REQUIREMENTS FOR THE DEGREE OF DOCTOR

OF PHILOSOPHY

FACULTY OF ENGINEERING

UNIVERSITY OF MALAYA

KUALA LUMPUR

2016

ii

UNIVERSITY OF MALAYA

ORIGINAL LITERARY WORK DECLARATION

Name of Candidate: Md. Moshiur Rahman (I.C/Passport No: OC2135616)

Registration/Matric No: KHA100041

Name of Degree: Doctor of Philosophy

Title of Thesis: STRUCTURAL HYBRIDIZATION AND ECONOMICAL

OPTIMIZATION OF STRENGTHENING SYSTEMS USED

FOR CONCRETE BEAMS

Field of Study: Structural Engineering

I do solemnly and sincerely declare that:

(1) I am the sole author/writer of this Work;

(2) This Work is original;

(3) Any use of any work in which copyright exists was done by way of fair dealing

and for permitted purposes and any excerpt or extract from, or reference to or

reproduction of any copyright work has been disclosed expressly and

sufficiently and the title of the Work and its authorship have been

acknowledged in this Work;

(4) I do not have any actual knowledge nor do I ought reasonably to know that the

making of this work constitutes an infringement of any copyright work;

(5) I hereby assign all and every rights in the copyright to this Work to the

University of Malaya (“UM”), who henceforth shall be owner of the copyright

in this Work and that any reproduction or use in any form or by any means

whatsoever is prohibited without the written consent of UM having been first

had and obtained;

(6) I am fully aware that if in the course of making this Work I have infringed any

copyright whether intentionally or otherwise, I may be subject to legal action

or any other action as may be determined by UM.

Candidate’s Signature Date:

Subscribed and solemnly declared before,

Witness’s Signature Date:

Name:

Designation:

iii

ABSTRACT

Strengthening of an existing structure is often necessary to increase its load carrying

capacity to meet new strength and serviceability requirements. However, strengthening

can lead premature failure and efficient usage of the strengthening materials should be

emphasized. Therefore, an efficient strengthening method along with the preparation of

relevant design guidelines is urgently required. To address this issue a combination of

external bonding reinforcement (EBR) and Near Surface Mounting (NSM) technique was

developed and tested in this study. The proposed technique is called the hybrid

strengthening method (HSM). In this study, efficient approach of strengthening

reinforced concrete beam were also studied along with introduction of HSM. To prevent

premature failure the use of end anchorage, shear strengthening and side HSM were

employed. In order to make strengthening method efficient, steel bar with cement mortar

was also used to replace the fibre reinforced polymer (FRP) and epoxy. Semi-numerical

and finite element models were developed and validated with the experimental results to

be used in the preparation of design guidelines. To help the designer reduce the

strengthening cost further, mathematical design optimization techniques are also

presented.

For this study, thirty-three reinforced concrete beams were cast and tested. These were

designed to address the objectives described above. The strengthening materials used

comprised of steel bars, steel plates and CFRP composites with different dimensions were

used for strengthening. The beams were extensively instrumented to monitor loads,

deflections, and strains. The beams were subjected to static and fatigue loadings.

Semi-numerical models were formulated to initiate the preparation of the design

procedure of the HSM beam. In these models, an analytical approach was made with the

help of the genetic algorithm optimization procedure to avoid time-consuming trial and

iv

error. In addition, finite element models (FEM) from the ABAQUS package to predict

flexural strength and deflection were used to do the parametric study. In the mathematical

design optimization method, the strengthening cost was minimized using non-linear

programming and genetic algorithms where flexural strength and serviceability

requirements were used as the major constraints.

From the experimental results, the HSM beam, in general, gave about 65% higher

flexural capacities as compared to the control beam at best. In terms of the efficiency, the

HSM beams showed a 36% increase in flexural capacities as compared to the EBR beam.

The partial replacement of epoxy adhesive with cement mortar in NSM strengthening

reduced costs without significantly affecting the flexure performance. The fatigue

performance of the HSM strengthened beam was found to be at least 6.5% higher than

that of the NSM strengthened beam. The semi-numerical and finite element models were

shown to be able to give consistent results as compared to the experimental results. The

application of the optimization method led to savings of up to 8% in the amount of

strengthening materials used as compared to classical design solutions.

v

ABSTRAK

Pengukuhan sesuatu struktur sedia ada selalunya diperlukan untuk meningkatkan

kapasiti beban bagi memenuhi keperluan kekuatan dan servis baru. Namun, pengukuhan

boleh menyebabkan kegagalan pra-matang dan penggunaan bahan pengukuhan yang

efisien patut diutamakan. Oleh itu, teknik pengukuhan yang efisien berserta dengan

penyediaan garis panduan rekabentuk yang berkaitan adalah sangat diperlukan. Untuk

menyelesaikan isu ini, satu kombinasi pemasangan pengukuhan luaran (EBR) dan juga

teknik pemasangan berhampiran permukaan (NSM) telah dihasilkan dan diuji dalam

kajian ini. Teknik ini dinamakan sebagai teknik pengukuhan hibrid (HSM). Dalam kajian

ini, kaedah yang efisien untuk pengukuhan rasuk bertetulang konkrit juga telah dikaji

berserta dengan pengenalan kepada HSM. Untuk mengelakkan kegagalan pra-matang

penggunaan labuh pada hujung, pengukuhan ricih dan HSM jenis sisi telah digunakan.

Untuk menghasilkan teknik pengukuhan yang efisien, batang besi dengan mortar simen

telah digunakan untuk menggantikan serat polimer bertetulang (FRP) dan epoxy. Model-

model separa numerikal dan unsur terhingga telah dihasilkan dan disahkan dengan

keputusan eksperimental untuk digunakan dalam penyediaan garis panduan rekabentuk.

Untuk membantu mengurangkan kos pengukuhan, teknik rekabentuk optima jenis

matematik juga telah disediakan.

Dalam kajian ini, tiga puluh rasuk bertetulang konkrit telah dihasilkan dan dikaji.

Semuanya direkabentuk untuk menepati objektif yang diberikan di atas. Bahan teknik

pengukuhan yang digunakan adalah batang besi, papan besi dan juga komposit CFRP

dengan dimensi yang berbeza telah digunakan untuk pengukuhan. Rasuk-rasuk tersebut

telah dipasang instrumen untuk memonitor beban, pesongan dan keterikan. Rasuk-rasuk

tersebut kemudian dikaji di bawah beban statik dan beban letih.

vi

Model-model semi-numerikal telah dihasilkan bagi memulakan penyediaan garis

panduan rekabentuk rasuk HSM. Dalam model-model ini, satu kaedah analitikal telah

dihasilkan dengan bantuan prosedur pengoptimuman algorisma genetik untuk

mengelakkan teknik cuba dan gagal yang memakan masa. Di samping itu, model-model

unsur terhingga (FEM) daripada ABAQUS untuk mengira kekuatan lenturan dan

pesongan telah digunakan untuk melakukan kajian parametric. Dalam kaedah rekabentuk

pengoptimuman matematik, kos pengukuhan telah dikurangkan dengan menggunakan

program tidak linear dan algorisma genetik di mana kekuatan lenturan dan keperluan

servis telah digunakan sebagai kekangan utama.

Daripada keputusan eksperimen, rasuk HSM memberikan kapasiti lenturan yang 65%

lebih tinggi berbanding rasuk kawalan. Dari segi kecekapan, rasuk HSM memberikan

36% peningkatan kekuatan lenturan berbanding rasuk EBR. Penggantian sebahagian

daripada gam epoxy dengan mortar simen dalam teknik pengukuhan NSM telah

mengurangkan kos tanpa mengubah prestasi lenturan dengan ketara. Prestasi keletihan

untuk rasuk HSM didapati adalah sekurang-kurangnya 6.5% lebih tinggi berbanting rasuk

NSM. Model-model semi-numerikal dan model unsur terhingga ditunjukkan mampu

memberi keputusan yang konsisten dengan keputusan eksperimental. Applikasi teknik

pengoptimuman memberikan penjimatan sebanyak 8% dari segi jumlah bahan

pengukuhan yang digunakan berbanding teknik rekabentuk klasik.

vii

ACKNOWLEDGEMENTS

In the Name of Allah, the Beneficent, the Merciful, I would like to express my utmost

gratitude and thanks to the Almighty Allah (s.w.t) for the help and guidance that He has

given me all these years.

I would like to express my sincere appreciation and gratitude to my supervisor,

Professor Ir. Dr. Mohd Zamin Bin Jumaat for his excellent supervision, guidance,

encouragement and support in carrying out this research work. I am deeply indebted to

him.

I would also like to express my great appreciation to University Malaya High Impact

Research Grant for funding this research work.

Last but not least, I would like to thank all my fellow postgraduate students for helping

me and for giving me suggestions, ideas, and advice during the course of this study.

viii

TABLE OF CONTENTS

ABSTRACT .................................................................................................................. III

ABSTRAK ...................................................................................................................... V

ACKNOWLEDGEMENTS ........................................................................................ VII

TABLE OF CONTENTS .......................................................................................... VIII

LIST OF FIGURES .................................................................................................. XIII

LIST OF TABLES ................................................................................................. XVIII

LIST OF SYMBOLS ................................................................................................. XIX

LIST OF ABBREVIATIONS ................................................................................... XXI

CHAPTER 1: INTRODUCTION .................................................................................. 1

1.1 Research Background .......................................................................................... 1

1.2 Goal and objectives of the Study .......................................................................... 8

1.3 Research Methodology ........................................................................................ 9

1.4 Chapter Outline ................................................................................................... 9

CHAPTER 2: LITERATURE REVIEW .................................................................... 11

2.1 Introduction ....................................................................................................... 11

2.2 Experimental Investigations on Structural Strengthening ................................... 11

2.2.1 External Bonding Reinforcement (EBR) ............................................ 12

2.2.2 Limitations of EBR System ................................................................ 15

2.2.3 Eliminating Premature Debonding in EBR ......................................... 18

2.2.4 Near Surface Mounting (NSM) Technique ......................................... 23

2.2.5 Limitations of NSM Technique .......................................................... 28

2.2.6 Fatigue Performance of EBR and NSM Technique ............................. 31

2.2.6.1 Strengthened with Steel............................................................. 31

2.2.6.2 Strengthened with FRP ............................................................. 32

2.3 Numerical Modelling ......................................................................................... 40

2.4 Optimization in Structural Design ...................................................................... 43

2.4.1 Gradient-Based Approach .................................................................. 43

2.4.2 Gradient-Free Approach ..................................................................... 44

2.4.3 Genetic Algorithms ............................................................................ 45

2.4.4 Optimization of RC Structures ........................................................... 47

ix

2.4.5 Optimization of FRP Strengthened RC Beams ................................... 50

2.5 Identification of Research Gaps and Significance of this Study .......................... 51

2.6 Research Questions ............................................................................................ 52

METHODOLOGY ............................................................................... 53

3.1 Introduction ....................................................................................................... 53

3.2 Experimental Programme ................................................................................... 53

3.2.1 Materials Used and Their Properties ................................................... 54

3.2.1.1 Concrete and Cement Mortar .................................................... 54

3.2.1.2 Internal Steel Reinforcement ..................................................... 55

3.2.1.3 Steel Plate ................................................................................. 55

3.2.1.4 CFRP Plate and Fabrics ............................................................ 55

3.2.1.5 Adhesive ................................................................................... 56

3.2.2 Design and Preparation of Beam Specimen ........................................ 57

3.2.3 Strengthening of RC Beams ............................................................... 59

3.2.3.1 Surface Preparation ................................................................... 59

3.2.3.2 Placement of Strengthening Materials ....................................... 62

3.2.4 Instrumentation .................................................................................. 62

3.2.4.1 Demec Points ............................................................................ 62

3.2.4.2 Electrical Resistance Strain Gauges .......................................... 63

3.2.4.3 Linear Variable Displacement Transducers (LVDTs) ................ 65

3.2.4.4 Data Logger .............................................................................. 65

3.2.4.5 Digital Extensometer ................................................................ 66

3.2.4.6 Dino-lite Digital Microscope ..................................................... 66

3.2.5 Test Setup and Procedure ................................................................... 67

3.2.6 Test Matrix ........................................................................................ 68

3.3 Development of Semi-numerical Model ............................................................. 73

3.3.1 Material Properties ............................................................................. 74

3.3.1.1 Concrete ................................................................................... 74

3.3.1.2 Steel Bars and Plates ................................................................. 75

3.3.1.3 CFRP Composite ...................................................................... 76

3.3.2 Modeling Methodology ...................................................................... 76

3.3.3 Deflection Prediction Model .............................................................. 78

3.3.3.1 Steps to Predict the Deflection: ................................................. 78

3.3.3.2 Semi-numerical Approach ......................................................... 79

3.3.4 Flexural Strength Model ..................................................................... 80

3.3.5 Debonding Strength Model ................................................................ 80

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3.3.5.1 Modelling Methodology............................................................ 80

3.3.5.2 Failure Criteria for Debonding Failure ...................................... 82

3.4 Finite Element Modelling .................................................................................. 84

3.4.1 Introduction ....................................................................................... 84

3.4.2 Material Properties and their Constitutive Model ................................ 85

3.4.2.1 Concrete ................................................................................... 85

3.4.2.2 Reinforcement .......................................................................... 86

3.4.2.3 Carbon Fiber Reinforced Polymer ............................................. 86

3.4.3 Boundary Conditions ......................................................................... 87

3.4.4 Loads on RC Beams ........................................................................... 88

3.4.5 Discretization ..................................................................................... 88

3.4.6 Finite Element Procedure ................................................................... 89

3.5 Mathematical Optimization ................................................................................ 90

3.5.1 Algorithm for Optimum Design Solution ........................................... 90

3.5.2 Objective Function ............................................................................. 91

3.5.3 Design Constraints ............................................................................. 93

3.5.3.1 Flexural Constraints .................................................................. 93

3.5.3.2 The Constraints against Separation Failure ................................ 95

3.5.3.3 Serviceability Constraints ......................................................... 97

3.5.4 Application of Optimization Method .................................................. 98

3.5.4.1 Non-linear Programming .......................................................... 98

3.5.4.2 Genetic Algorithm .................................................................... 98

RESULTS AND DISCUSSION ........................................................ 100

4.1 Introduction ..................................................................................................... 100

4.2 Result of Experimental Investigation ............................................................... 100

4.2.1 Material Properties ........................................................................... 100

4.2.2 Experimental Behaviour of Steel HSM Strengthened Beams ............ 101

4.2.2.1 Load Carrying Capacity and Failure Mode .............................. 101

4.2.2.2 Effect of Strengthening on Deflection and Cracking

Behaviour ............................................................................... 107

4.2.2.3 Comparison of HSM with EBR using Steel Plates and Bars .... 108

(a) Effect of HSM strengthening on Ultimate Load ................. 108

(b) Deflection Characteristics .................................................. 109

(c) Cracking Behaviour ............................................................ 111

(d) Internal Reinforcing Bar Strain .......................................... 111

(e) Efficiency of HSM ............................................................... 112

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4.2.2.4 Effect of Plate and Bar Length, Bar Dia. and No. of Grooves .. 113

(a) Effect of Plate and Bar Length ........................................... 113

(b) Effect of Bar Diameter ........................................................ 114

(c) Effect of Number of Bars or NSM Grooves ........................ 116

4.2.3 Experimental Behaviour of CFRP-HSM Strengthened Beam ........... 116

4.2.3.1 Load Carrying Capacity and Failure Mode .............................. 116

4.2.3.2 Effect of Strengthening on Deflection and Cracking

Behaviour ............................................................................... 120

4.2.3.3 Comparison of HSM with EBR ............................................... 121

(a) Effect of HSM Strengthening on Ultimate Load ................. 121

(b) Deflection Characteristics .................................................. 122

(c) Cracking Behaviour ............................................................ 124

(d) Internal Reinforcing Bar Strain .......................................... 124

4.2.3.4 Effect of Plate and Bar Length, Bar Dia. and No. of Grooves .. 125

(a) Effect of Plate and Bar Length ........................................... 125

(b) Effect of Bar Diameter ........................................................ 126

(c) Effect of Number of Bars or NSM Grooves ........................ 127

4.2.4 Eliminating End Debonding ............................................................. 128

4.2.4.1 Effect of Plate Thickness ........................................................ 128

4.2.4.2 Effect of Shear Strengthening ................................................. 129

4.2.4.3 Effect of End Anchorage ......................................................... 130

4.2.4.4 Effect of Location of the Steel Plate and Bar ........................... 130

4.2.5 Experimental Behaviour of Steel NSM Strengthened Beam ............. 130

4.2.5.1 Load Carrying Capacity and Failure Mode .............................. 130

4.2.5.2 Effect of Strengthening on Deflection, Crack and Strain ......... 135

4.2.5.3 Effect of Different Parameters ................................................. 137

(a) Effect of Adhesive Type ....................................................... 138

(b) Effect of Partial Epoxy Replacement with Cement Mortar 139

(c) Effect of Number of NSM Grooves ..................................... 141

(d) Effect of Bar Numbers with the Same Diameter ................. 143

(e) Effect of Internal Reinforcement ......................................... 145

4.2.5.4 Comparison of NSM with EBR ............................................... 145

4.2.6 Fatigue Performance of the HSM Strengthened Beam ...................... 146

4.2.6.1 Failure Mode .......................................................................... 146

4.2.6.2 Number of Cycles to Failure ................................................... 148

4.3 Verification of Semi-numerical Model ............................................................. 149

4.3.1 Verification of Flexural Strength Model ........................................... 149

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4.3.2 Verification of Deflection Prediction Model ..................................... 150

4.3.3 Verification of Debonding Strength Model ....................................... 151

4.3.4 Parametric Study using Debonding Strength Model .......................... 151

4.4 Finite Element Numerical Results .................................................................... 153

4.4.1 Load Carrying Capacities ................................................................. 153

4.4.2 Load-Deflection Relationship ........................................................... 156

4.4.3 Parametric Study using Finite Element Modelling ............................ 158

4.5 Solution of Mathematical Optimization ............................................................ 160

4.5.1 Non-linear Programming Solutions .................................................. 160

4.5.2 Genetic Algorithm Solutions ............................................................ 161

4.6 Summary of the Results and Discussion ........................................................... 163

CONCLUSIONS AND RECOMMENDATIONS ........................... 165

5.1 Conclusions ..................................................................................................... 165

5.2 Recommendations ............................................................................................ 167

REFERENCES ............................................................................................................ 168

Test Results for Concrete and Steel Properties ............................... 183

Necessary Calculations .................................................................. 187

Experimental and Numerical load deflection Curves ...................... 192

LIST OF PUBLICATIONS AND PAPERS PRESENTED .................................... 204

xiii

LIST OF FIGURES

Figure 2.1 : Strengthened RC beams tested by Attari et al. (2012) ............................... 15

Figure 2.2. Different failure modes of EBR system ..................................................... 15

Figure 2.3: EBROG technique (Mostofinejad & Shameli, 2013) ................................. 26

Figure 2.4: Failure modes of beams strengthened with NSM CFRP bars ..................... 27

Figure 2.5: Failure mode of the NSM technique (Lorenzis & Teng, 2007)................... 29

Figure 3.1: Fiber in matrix (Badawi, 2007) ................................................................. 56

Figure 3.2: Details of the beam specimens .................................................................. 57

Figure 3.3: Prepared surface of a concrete beam ......................................................... 59

Figure 3.4: Compressed air jetting............................................................................... 60

Figure 3.5: Sand blasted steel plate ............................................................................. 60

Figure 3.6: Groove cutting .......................................................................................... 61

Figure 3.7: Demec points on a concrete beam with a strain gauge ............................... 63

Figure 3.8: Surface preparation of steel bars to place strain gauges ............................. 63

Figure 3.9: Attachment of strain gauges ...................................................................... 64

Figure 3.10: Strain gauges covered with silicone gel ................................................... 65

Figure 3.11: Dino-lite digital microscope for crack width measurement ...................... 66

Figure 3.12: Experimental set up ................................................................................. 67

Figure 3.13: Series CB beam (Control beam) .............................................................. 71

Figure 3.14: Series P (EBR) ........................................................................................ 71

Figure 3.15: Series N (NSM strengthening)................................................................. 71

Figure 3.16: Series H (HSM strengthening). ................................................................ 71

Figure 3.17: Cross-section of series SH beam (HSM at sides) ..................................... 72

Figure 3.18 : Stress-strain relationship of concrete (Bangash, 1989) ............................ 74

xiv

Figure 3.19: Stress-strain relationship of steel bar and plate ........................................ 75

Figure 3.20: Strain, stress and force distribution on a section ...................................... 77

Figure 3.21: The principle and interfacial stress .......................................................... 82

Figure 3.22: Typical biaxial failure criteria for concrete (Tysmans et al., 2015) .......... 83

Figure 3.23: Stress-strain diagram of CFRP ................................................................ 87

Figure 3.24: Function plot depicting optimum for a two design variable set ................ 92

Figure 3.25: Stress and strain distribution of balanced failure ...................................... 94

Figure 4.1: Debonding failure mode of H1B8S19L73W2T ....................................... 103

Figure 4.2: Debonding failure mode of H1B8S16L73W2T ....................................... 103

Figure 4.3: Debonding failure mode of H1B6S16L73W2T ....................................... 104

Figure 4.4: Debonding failure mode of H2B8S19L73W2T ....................................... 104

Figure 4.5: Debonding failure mode of H2B6S19L73W2T ....................................... 104

Figure 4.6: Debonding failure mode of H2B6S19L73W2.76T................................... 105

Figure 4.7: Debonding failure mode of H2B6S19L125W2T ..................................... 105

Figure 4.8: Debonding failure mode of H1B8SD19L73W2T..................................... 105

Figure 4.9: Flexure failure mode of H2B6S19L125W1.5T ........................................ 106

Figure 4.10: Flexure failure mode of H1B8S19L73W2TAS ...................................... 106

Figure 4.11: Flexure failure mode of H1B8S19L73W2TAF ...................................... 106

Figure 4.12: Flexure failure mode of SH2B6S19L100W2T ....................................... 107

Figure 4.13: Comparison of failure load between HSM and EBR .............................. 109

Figure 4.14 : Load-deflection of CB, H1B8S19L73W2T and PS19L73W2.76T. ....... 110

Figure 4.15: Load-deflection of CB, H1B8S16L73W2T and PS16L73W2.76T ......... 110

Figure 4.16: Improvement of first crack loading in HSM strengthening .................... 111

Figure 4.17: Efficiency of the HSM .......................................................................... 113

xv

Figure 4.18: The effect of plate and bar length on failure load ................................... 114

Figure 4.19: The effect of bar diameter ..................................................................... 115

Figure 4.20: The effect of number of bars or grooves ................................................ 116

Figure 4.21: Debonding failure mode of H1B8F19L80W1.2T .................................. 118

Figure 4.22: Debonding failure mode of H1B8F16L80W1.2T .................................. 118

Figure 4.23: Debonding failure mode of H1BP8F16L80W1.2T ................................ 118

Figure 4.24: Debonding failure mode of H1BP6F16L80W1.2T ................................ 119

Figure 4.25: Debonding failure mode of H2BP6F16L80W1.2T ................................ 119

Figure 4.26: Flexure failure mode of H1B8F19L80W1.2TAF ................................... 119

Figure 4.27: Flexure failure mode of H1B6FR19L100W.17T ................................... 120

Figure 4.28: Comparison of Ultimate load between HSM and EBR .......................... 122

Figure 4.29: Load-deflection of CB, H1B8F19L80W1.2T and PF19L80W1.2T ........ 123

Figure 4.30: Load-deflection of CB, H1B8F16L80W1.2T and PF16L80W1.2T ........ 123

Figure 4.31: Improvement in first crack loads of HSM strengthened CFRP beams .... 124

Figure 4.32: The effect of plate and bar length on failure load ................................... 126

Figure 4.33: The effect of bar diameter ..................................................................... 127

Figure 4.34: The effect of number of grooves on failure load .................................... 128

Figure 4.35: The effect of plate thickness. ................................................................. 129

Figure 4.36: Failure mode of control beam ................................................................ 132

Figure 4.37: Failure mode of N2S6C ......................................................................... 132

Figure 4.38: Failure mode of N2S6E ......................................................................... 133

Figure 4.39: Failure mode of N2S6EC ...................................................................... 133

Figure 4.40: Failure mode of N1S8E ......................................................................... 133

Figure 4.41: Failure mode of N1S8C ......................................................................... 134

xvi

Figure 4.42: Failure mode of N3S8C ......................................................................... 134

Figure 4.43: Failure mode of N1SH8C ...................................................................... 134

Figure 4.44: Failure mode of N2SS8C ...................................................................... 135

Figure 4.45: The effect of adhesive type on first crack and failure load ..................... 138

Figure 4.46: Load-deflection diagram of CB, N2S6C and N2S6E ............................. 139

Figure 4.47: Bond stresses in the longitudinal plane (De Lorenzis & Teng, 2007) ..... 140

Figure 4.48: The effect of partial replacement of epoxy with cement mortar ............. 141

Figure 4.49: Load-deflection diagram of CB, N2S6E and N2S6EC ........................... 141

Figure 4.50: The effect of number of grooves............................................................ 142

Figure 4.51: Load-deflection of CB, N2S6C and N1S8C with cement mortar ........... 143

Figure 4.52: Load-deflection diagram of CB, N2S6E and N1S8E ............................. 143

Figure 4.53: The effect of bar number on the performance of NSM beam ................. 144

Figure 4.54: Load-deflection diagram of CB, N1S8C and N3S8C ............................. 145

Figure 4.55: Comparison of NSM with EBR ............................................................. 146

Figure 4.56: Fatigue failure mode of control beam .................................................... 147

Figure 4.57: Fatigue fracture of steel ......................................................................... 147

Figure 4.58: Failure mode of NSF ............................................................................. 147

Figure 4.59: Failure mode of PSF ............................................................................. 148

Figure 4.60: Failure mode of HSF ............................................................................. 148

Figure 4.61: Predicted and experimental failure load ................................................. 149

Figure 4.62: Predicted and experimental load-deflection diagram of CB ................... 150

Figure 4.63: Predicted and experimental load-deflection of H1B8S19L73W2T ......... 150

Figure 4.64: Predicted and experimental debonding failure load ................................ 151

Figure 4.65: The effect of plate thickness using the debonding strength model .......... 152

xvii

Figure 4.66: The effect of plate length using the debonding strength model .............. 152

Figure 4.67: Meshing with deflected shape ............................................................... 153

Figure 4.68: Typical flexure failure mode of control beams (2D) .............................. 155

Figure 4.69: Typical flexure failure mode of NSM strengthened beams (2D) ............ 155

Figure 4.70: Typical debonding failure mode of HSM strengthened beam (2D) ........ 155

Figure 4.71 : Load deflection diagram of control beam ............................................. 156

Figure 4.72 : Typical Load deflection diagram of NSM strengthened beam ............... 157

Figure 4.73: Typical Load deflection diagram of HSM strengthened beam................ 157

Figure 4.74: The effect of plate thickness using FEA ................................................ 159

Figure 4.75: The effect of plate length using FEA ..................................................... 159

xviii

LIST OF TABLES

Table 2.1: Summary literature review on EBR ............................................................ 13

Table 3.1: Concrete mix design ................................................................................... 54

Table 3.2: Test matrix1 ............................................................................................... 69

Table 3.3: Test matrix2 (Taken from Alam (2010)) ..................................................... 71

Table 3.4: Description of beam notation for HSM. ...................................................... 72

Table 3.5: Description of beam notation for NSM strengthening. ................................ 72

Table 4.1: The properties of steel bar ........................................................................ 101

Table 4.2: First crack, yield and failure (and modes) load of HSM-steel .................... 102

Table 4.3: Reduction in deflection due to HSM strengthening ................................... 107

Table 4.4: Bar strain at different service loads ........................................................... 112

Table 4.5: First crack, yield and failure (and modes) load of HSM-CFRP ................. 117

Table 4.6: Reduction in deflection due to HSM strengthening with FRP ................... 120

Table 4.7: Bar strain at different service loads ........................................................... 125

Table 4.8: First crack, yield and failure (and mode) of NSM beams .......................... 131

Table 4.9: Reduction in deflection due to NSM strengthening ................................... 136

Table 4.10: Reduction of strain in steel rebars due to NSM strengthening ................. 137

Table 4.11: Reduction in concrete strain due to NSM strengthening .......................... 137

Table 4.12: Result of fatigue test ............................................................................... 149

Table 4.13: The comparison between numerical and experimental results ................. 154

Table 4.14 : The common data used for calculation ................................................... 161

Table 4.15 : Result of FRP strengthening using non-linear programming .................. 161

Table 4.16 : Result of FRP strengthening using the genetic algorithm ....................... 162

Table 4.17: Achievement of Objectives ..................................................................... 164

xix

LIST OF SYMBOLS

a : The depth of stress block

ae : Edge clearance

ag : Clear spacing of NSM grooves

As : Cross sectional area of steel bar

Af : Cross sectional area of plate

b : Width of the concrete beam specimen

bf : Width of strengthening plate

C : Total cost of strengthening system

CF : Cost of carbon fiber reinforced polymer plate

Ca : Cost of adhesive

d : Effective depth of concrete beam specimen

dc Depth of concrete cover

dx Depth of compressive force carried out by concrete

Ec : Modulus elasticity of concrete

Ep : Modulus elasticity of strengthening plate

Es : Modulus elasticity of steel bar

ε : Strain

εc : Strain of concrete

εcu : Ultimate strain of concrete

εnsm : Strain of NSM bar

εp : Strain of strengthening plate

εs : Strain of main tensile steel

Fcc : The force carried by the concrete

Εfu : The ultimate strain of FRP

xx

Fnsm : The force carried by the NSM steel bar

Fp : The force carried by the strengthening plate

Fs : The force carried by the steel bar

fy : Yield strength of steel bar

h : Height of the concrete beam specimen

l : Span length

Lf : Length of the strengthening plate

M : Moment

m : Meter

Mr : Resisting bending moment

Mr,b : Balance moment of resistance

tf : Thickness of the strengthening plate

Vc : Shear capacity of the concrete

Vcap : Shear capacity of the beam

Vs : Shear capacity of the steel bar

w : Uniformly distributed load

c : Depth of neutral axis

z : Lever arm

xxi

LIST OF ABBREVIATIONS

ACI : American Concrete Institute

ACO : Anti-Colony Optimization

CFRP : Carbon Fiber Reinforced Polymer

EMPA : Swiss Federal Laboratories For Materials Science And Technology

EBR : External Bonded Reinforcement

FEA : Finite Element Analysis

FEM : Finite Element Modeling

FHB : Friction Hybrid Bonded

FRP : Fiber Reinforced Polymer

GA : Genetic Algorithm

HF : Beam Strengthened with CFRP using HSM

HS : Beam Strengthened with Steel using HSM

HSM : Hybrid Strengthening Method

JSCE : Japan Society of Civil Engineering

LVDT : Linear Variable Displacement Transducer

NLP : Non Linear Programming

NSM : Near Surface Mounting

PF : Beam Strengthened with CFRP using EBR

PS : Beam Strengthened with Steel using EBR

PSO : Particle Swarm Optimization

RC : Reinforced Concrete

1

CHAPTER 1: INTRODUCTION

1.1 Research Background

Rehabilitation and strengthening of reinforced concrete (RC) structures are some of

the major challenges for structural engineers today. The strengthening of RC structures is

a dynamically growing division of structural engineering and in recent years, there has

been an increase in the application of new repair and strengthening systems for RC load-

carrying structures. In most cases, it is an increase in dead and live loading that has to be

safely carried by the structures, as well as their poor technical performance that

necessitates the use of strengthening procedures.

The main reasons why structural strengthening is done are to:

i. Safely accommodate increases in dead and live loading,

ii. Counter material aging and corrosion,

iii. Offset mechanical damage,

iv. Reduce strain limits in order to maintain composite action,

v. Decrease stress in steel reinforcement for fatigue consideration,

vi. Decrease crack widths to maintain serviceability,

vii. Modify a structure’s static scheme to adapt to a changed situation, and

viii. Overcome construction failures.

Structures that have been built more than several decades ago often require

strengthening and upgrading to meet current service load demands. Thus, the use of

strengthening techniques is expected to grow rapidly over the next few years. Several

methods of strengthening RC structures using various materials have been studied and

applied in the rehabilitation field (Eberline et al., 1988; Juozapaitis et al., 2013;

Macdonald & Calder, 1982). However, no solution can be applied to all cases as each

specific structure must be approached on an individual basis (Kamiński & Trapko, 2006).

2

Selection of the proper strengthening method requires careful consideration of many

factors including the following engineering issues:

i. Amount of the required increase in strength.

ii. Effect of variations in relative stiffness.

iii. Size of the works.

iv. Environmental situations (adhesives might not be suitable for use in high-

temperature environments; external steel may not be suitable in corrosive

environments).

v. In-situ concrete strength and substrate integrity.

vi. Constraints dimension or clearance.

vii. Accessibility.

viii. Operational limitations.

ix. Availability of local materials, equipment, and experienced contractors.

x. Construction, maintenance and life cycle costs.

One technique commonly used to enhance the strength or serviceability of RC

structures is the gluing of steel or CFRP plates to the outer surfaces of the structures. This

method has been employed universally since the late 1960s (Hermite & Bresson, 1967).

However, the use of this technique usually suffers from premature failure like plate end

separation, intermediate crack induced debonding or shear failure. This debonding can

cause serious brittle and catastrophic failure before the strengthened beam reaches its

ultimate capacity.

Many studies have been conducted to find solutions to this brittle debonding and to

reduce the interfacial stresses between the RC substrate and the strengthening plate

(Fitton & Broughton, 2005; Hildebrand, 1994). One remedy was to change the thickness

of the steel or FRP plate or the joint geometry by tapering the plate (Tsai & Morton,

3

1995). Although the use of geometrical variations to the plate ends by tapering the form

is a useful tool to reduce the stresses in adhesive joints, it is a complex, time consuming

and costly process. This solution aims to control the allowable strain in FRP plates to a

threshold value to prevent debonding but the results of this approach are not efficient

(Radfar et al., 2012).

More recently, near surface mounted (NSM) reinforcement has been the subject of

fascination in an increasing amount of research as well as realistic application because it

is less prone to premature debonding (De Lorenzis & Teng, 2007). However, there are

some limitations to its application. Sometimes, the width of the beam may not be

sufficiently wide to provide necessary edge clearance and clear spacing between two

adjacent NSM grooves. ACI 440 recommends that the minimum edge clearance and clear

spacing for the NSM grooves should be four and two times the groove depth, respectively.

However, this recommendation has also been proven to be inadequate by Lorenzis (2002).

Additionally, the thickness of the concrete cover should be high enough to provide

sufficient groove depth.

The use of NSM steel bars to strengthen RC structures started in Europe in the early

fifties (Lorenzis & Nanni, 2002). The earliest reference to this technique dates back to

1949 (Asplund, 1949), where steel bar with cement grout was used to strengthen a

concrete slab in field construction work. More recent use of NSM steel bars for the

strengthening of masonry structures and arch bridges have also been documented

(Garrity, 2001). Most experimental studies on this strengthening technique investigate

the flexural behaviour of concrete beams strengthened using NSM FRP bars or strips (Al-

Mahmoud et al., 2009; Badawi & Soudki, 2009; El-Hacha & Rizkalla, 2004a; Lorenzis

et al., 2000; Soliman et al., 2010). The test results confirm that NSM FRP bars can be

applied to increase the flexural capacity of RC elements. However, little or no

4

experimental investigation has been done on the flexural behaviour of concrete beams

strengthened with NSM steel bars.

The present research work would like to present a hybridization of the above two

strengthening methods in order to address the shortcomings of both methods. This

hybridization combines the externally bonded reinforcement (EBR) with the NSM

technique so that they complement each other and mutually reduce their limitations. This

method is called the hybrid strengthening method (HSM). Previous research has shown

that decrease in plate thickness reduces the magnitude of stress concentration at the plate

extremities. Instead of tapering the plate, this new bonding method could make it possible

to reduce the plate thickness by transferring a portion of the required amount of

strengthening material from the EBR to the bars in the NSM technique. Consequently,

the size or number of NSM bars required can also be reduced by sharing the amount of

strengthening material needed with the plate in the EBR. This can then ensure enough

space for edge clearance and clear spacing of the NSM groove.

The main purpose of the HSM is to increase bond performance against plate end

debonding failure between the concrete substrate and the strengthening plates and bars.

Plate end debonding can probably be prevented or delayed through the reduction of

interfacial stress. The HSM method can reduce interfacial shear and normal stress in two

ways. The first way is by decreasing the thickness of the plate by transferring some of the

required material from the plate to the NSM system. After transferring, the total amount

of strengthening material used on the structure will be the same. However, the magnitude

of interfacial stress will be decreased due to reduced plate thickness. Plate thickness is

one of the most important parameters in reducing interfacial stress (Lousdad et al., 2010).

Most codes of practice (Fib, 2001; JSCE, 2001) also recommend limiting design strain

on the plate to eliminate debonding. Other studies (Maruyama & Ueda, 2001; Teng et al.,

5

2003) have confirmed similar limits. In most cases, the design debonding strains are

inversely proportional to plate thickness. For a fixed FRP ratio, the debonding potential

has been shown to increase significantly with increasing FRP thickness (Garden et al.,

1997). Although the above studies used FRP plates for strengthening, the findings are

also applicable to strengthening with steel plates.

Several studies have focused on steel plate end debonding. Swamy et al. (1987b)

showed that premature end debonding of steel plates can be avoided by increasing the

aspect ratio of the plate by more than fifty. Swamy and Mukopadhyaya (1995) have

demonstrated that this criteria holds true for FRP plates when glass, glass-carbon, and

aramid fibers are applied. Oehlers (1992) proposed a formula based on the interaction

between flexural and shear capacities of the beam where the debonding failure moment

is inversely proportional to plate thickness. Zibra et al. (1994) presented a model based

on the shear capacity of the beam where debonding shear force decreases width steel plate

thickness. Hassanen and Raoof (2001) proposed that design strain on the plate is inversely

proportional to plate thickness. Therefore, reducing plate thickness is an effective way to

prevent plate debonding.

The second way, the HSM method can reduce interfacial stress by increasing the

surface area in contact between the strengthening plate and the concrete face. The HSM

involves cutting grooves along the beam for NSM strengthening. The grooves increase

the bonding surface area between the plate and the concrete substrate. As stress is equal

to load divided by the corresponding surface area, an increase in surface area will decrease

interfacial shear stress. Moreover, the addition of adhesive in the NSM grooves in the

hybrid strengthening system further improves bond performance between the

strengthening plate and the concrete substrate.

6

In order to confirm the advantages of the HSM mentioned above, the structural

performance of the RC beam strengthened with the new method needs to be fully

characterized. Even though there are some test data on the structural behaviour of

strengthened beams using the above two existing methods, it is difficult to find any test

data on the experimental behaviour of strengthened beams using hybridization of the EBR

and the NSM technique. The HSM has the potential to take advantage of both methods

and complementarily eliminate their respective shortcomings. Therefore, the HSM could

become an effective and efficient method to strengthen structural members through

proper utilization of materials.

Proper utilization of materials is an important parameter in the constructing and

strengthening of structures. There is an increasing demand to reduce construction costs

of structures to cope with universal competition and this has encouraged structural

engineers to find more efficient structural strengthening systems. A number of design

guidelines have been published in different countries for the design of RC structures

strengthened with FRP. However, the design of RC beams and their structural

strengthening systems involves performing preliminary elastic analyses based on

assumed dimensions and then examining the member for its adequacy against strength,

serviceability and other requirements as imposed by the design codes. If the requirements

are not satisfied, then the cross-sections are modified repeatedly until they satisfy the

requirements of the codes. This process is carried out repetitively without consideration

of the relative costs of the structural strengthening system’s component materials. As a

result, a situation in which excessive material is used usually occurs, this results in higher

costs than necessary. A guideline is therefore required to determine the minimum amount

of materials needed to adequately strengthen a structure to maintain its functionality and

thus optimize the total cost of the structural strengthening system.

7

Material cost is an important factor in designing and implementing external

strengthening systems for RC structures. The main factors influencing the cost are the

amount of steel, FRP and adhesive to be used. Labor and formwork costs are also

significant. It is therefore necessary to make RC strengthening structures less expensive,

while still satisfying serviceability and strength criteria. Many researchers have used

several optimization techniques for the design of RC structures. Kanagasundaram and

Karihaloo (1991) formulated cost optimization as a non-linear programming problem.

Adamu et al. (1994) developed a method based on a continuum-type optimality criteria,

while Han et al. (1996) used discretized continuum-type optimality criteria. Leps and

Sejnoha (2003) used genetic algorithms to optimize RC beams while Camp et al. (2003)

used them for structures. However, no research has been found to optimize structural

strengthening except Perera and Varona (2009), where genetic algorithms were used for

discrete optimization.

Based on the discussion of the research background above, a number of research gaps

have been found and are summarized below:

i. Strengthening of RC beams using NSM steel bars lacks investigation.

ii. Effect of replacing epoxy adhesive with cement mortar on the behaviour of

NSM strengthened RC beams has not yet been studied.

iii. Hybridization of EBR with NSM technique is a potential research area.

iv. A design methodology for the HSM has yet to be devised.

v. Optimum design methods to strengthen RC beams are rare and limited.

The present study explores the use of steel bars and cements mortar in the NSM system

and develops a new structural strengthening method that combines the conventional EBR

with the NSM technique into a hybrid strengthening system. A number of RC beam

specimens are strengthened using different configurations of steel bars and steel or CFRP

8

plates, which are then subjected to static and fatigue loading. With extensive use of

instruments, the beams are constantly monitored for loading, deflections and strains over

the entire spectrum of loading to failure. The effects of different parameters on the

performance of the RC beams strengthened using the HSM are investigated implicitly.

The present research also utilizes optimization techniques coupled with advanced

computer aided tools in the process of creating conceptual and detailed designs of the

structural strengthening system. Therefore, the present study also describes the

development of an easy and efficient model for optimizing the design of FRP

strengthened RC beams. The model uses two mathematical methods, which are non-linear

programming and genetic algorithms. The use of the hybrid strengthening technique and

the optimum design method may lead to significant savings in the amount of component

materials used in strengthening as compared to classical solutions.

1.2 Goal and objectives of the Study

The ultimate goal of this study is to make a more efficient structural strengthening

system using newly proposed hybrid strengthening method (HSM). The efficiency of a

system can be defined as the performance divided by the corresponding cost of the

system. The performance of strengthening will be increased using two means: method

and material hybridization. The material hybridization will be achieved by the

replacement of epoxy adhesive with cement. The HSM will be a combination of the EBR

and NSM method. To reduce the cost of strengthening, the design will be optimized using

a mixture of genetic algorithm with non-linear programming. Therefore, the goal of this

research is supported by a number of objectives.

9

The objectives of this research work can be summarized as follows to:

i. Develop a strategy for eliminating premature failures of strengthened beams

including the introduction of the hybrid strengthening method (HSM).

ii. Study the effectiveness of using cement mortar to replace epoxy and steel

bar to replace FRP in the NSM strengthening method.

iii. Conveyance the fatigue performance of RC beams strengthened with HSM,

EBR, and NSM.

iv. Develop a semi-numerical model and finite element model (FEM) to predict

flexural strength and deflection of RC beams strengthened using the HSM.

v. Propose an economical approach for flexural strengthening of RC beams

with CFRP plate based on non-linear and genetic algorithms.

1.3 Research Methodology

Three methods are used to achieve the objectives of this research work. The three

methods are: conducting an experimental programme, developing a semi-numerical and

finite element model and using mathematical optimization. Extensive experimental

investigations were done to achieve the first to fourth objectives of this study as listed

above. To achieve the fifth objective, a semi-numerical model was formulated of the

strengthened beams and the original un-strengthened control beam. Similarly, a finite

element model was developed to achieve objective six. Mathematical programming and

an evolutionary algorithm-based optimization technique were applied to achieve the

seventh objective.

1.4 Chapter Outline

The thesis comprises of five chapters dealing with various aspects of strengthening RC

beams for static and fatigue loading. A brief outline follows:

10

Chapter 1 gives a general introduction of the research to be dealt with. A short research

background on recent advancement of strengthening RC beams is presented.

Accordingly, the goal, purposes, research objectives and brief methodology are discussed.

The chapter concludes with an outline of the thesis.

The second chapter presents a thorough review of relevant literature. A concise survey

is given of recent literature on the use of external bonding and the NSM technique to

strengthen RC beams under monotonic and fatigue loadings and on the application of

design optimization techniques.

The third chapter presents the experimental program, specimen fabrication, test

instrumentation and loading test set-up. The choices for the different parameters is

explained and justified. A methodology for the design optimization of RC beams

strengthened with FRP composites is also presented.

The fourth chapter presents the results and discussion. A description of the

performance of the strengthened beams under test conditions is qualitatively compared to

the behaviour of an un-strengthened control beam. The results are compared with the

findings of previous related studies. Observations and possible solutions for design

optimization are also discussed in this chapter.

Finally, the fifth chapter summarizes the main findings of the research work and

highlights conclusions. Recommendations for further research are also given in this

chapter.

The appendices present selected results in more detail, as well as necessary hand

computations for the research.

11

CHAPTER 2: LITERATURE REVIEW

2.1 Introduction

This chapter discusses existing works that are relevant to the objectives of the present

study, and identifies the gaps in the existing research that will be addressed by this study.

Furthermore, it presents the research questions of this study. This chapter has the

following six sections. Section 2.2 reviews experimental investigations on structural

strengthening, specifically the NSM reinforcement technique and the EBR method. The

limitations of each strengthening method are also discussed. In addition, this section

outlines various studies that have investigated the fatigue performance of RC beams

strengthened with steel or FRP, using either the NSM technique or the EBR method.

Section 2.3 reviews research on the numerical modelling of RC beams strengthened with

steel and FRP in order to predict flexural behaviour. Section 2.4 discusses works on the

optimization of the structural design of strengthened RC structures. Section 2.5 identifies

the gaps in research and points out the significance of the present study. Section 2.6

presents the research questions for this study.

2.2 Experimental Investigations on Structural Strengthening

Several materials and methods have been used for structural strengthening. The

common material used in strengthening includes spray concrete, ferro-cement, steel plate

and FRP. Diab (1998) reported the use of spray concrete. Romualdi (1987) and Iorns

(1987) introduced the use of ferro-cement, which was later utilized by Paramasivam et

al. (1998). However, the most frequently used materials for structural strengthening are

steel plate and FRP, of which FRP is especially promising. There are different types of

FRP, including carbon, glass and aramid. FRP can also be found in various forms such as

pultrusion plates, sheets and fabrics.

12

Common structural strengthening methods include section enlargement, external pre-

stressing, external bonding and near surface mounting (NSM). The technique of bonding

steel plates or carbon fibre reinforced polymer (CFRP) plates to the external surfaces of

RC structures to enhance their strength or serviceability has been employed worldwide

since the late 1960s (Hermite & Bresson, 1967). More recently, the NSM technique using

FRP has become the subject of fascination in a large amount of research and has many

practical uses.

2.2.1 External Bonding Reinforcement (EBR)

Research study into the behaviour of structural members strengthened with steel plates

was started concurrently in South Africa and France in the 1960s (Fleming & King, 1967;

Gilibert et al., 1976; Hermite & Bresson, 1967; Lerchenthal, 1967). The first application

of epoxy bonded steel plates for strengthening concrete beams was reported in 1964 in

Durban, South Africa. Further development of proper adhesives encouraged more

research work.

Preliminary research works were made by Irwin (1975), Macdonald (1978) and

Macdonald and Calder (1982). Macdonald and Calder (1982) made four-point loading

tests on RC beams strengthened with steel plates, 4900 mm in length. Strengthening with

steel plates of existing structures has also been studied in Switzerland at the Swiss Federal

Laboratories for Material Testing and Research (EMPA) (Ladner & Weder, 1981).

Bending tests were conducted on RC beams 3700 mm in length, and the effect of the plate

aspect ratio was studied while the plate area was kept constant. Summary studies on EBR

are given in Table 2.1

13

Table 2.1: Summary literature review on EBR

Sl.

no

Authors Parameters/

Variables

Findings

1 Jones et al. (1988) Type and size

of end

anchorage,

length

The different anchorage systems

caused no apparent variations on the

deflection performance of the beams.

The use of bolts did not prevent

debonding

2 Hussain et al. (1995) Effectiveness

of anchor bolt

Bolts were found to improve the

ductility of the plated beams

considerably, but to only marginally

effect the ultimate load capacity,

agreed with Jones et al. (1988)

3 Saadatmanesh and

Ehsani (1989)

Size of glass

FRP (GFRP)

Flexural strength increased with

increasing area of the GFRP sheets

4 Meier and Kaiser

(1991)

Effect of

strengthening

The beams doubled in strength, but

were less ductile as the reduced

deflections at failure, The CFRP

laminates also caused a more

distributed cracking pattern with

reduced crack widths. Other

researchers have subsequently found

similar results (Beber et al., 1999;

Heffernan & Erki, 1996; Jonaitis et

al., 1999; Kachlakev, 1999; Naaman,

1999; Swamy et al., 1996a; Swamy et

al., 1996b)

5 An et al. (1991) Internal steel

ratio, stiffness

of plate

beams with high internal steel ratios

were more effectively strengthened

using a stiffer plate with high strength

concrete than with a plate of lower

stiffness with low strength concrete.

Cha et al. (1999) found similar results

6 Triantafillou and

Plevris (1992)

Number of FRP

layer

The debonding of FRP limited the

number of FRP layers that could be

used.

7 Hutchinson and

Rahimi (1993)

FRP type and

thickness

Using either GFRP or CFRP

remarkably increased the flexural

capacity of RC beams.

8 Triantafillou and

Plevris (1995)

Reliability,

reduction

factors

They proposed a general strength

reduction factor of 0.85 and a partial

reduction factor of 0.95 for FRP

strength.

9 White et al. (1998) Loading rates Service and ultimate flexural

capacity increased as the rate of

loading increased. Cracking and

14

failure modes were not affected by

the rate of loading

10 Toutanji et al. (2001) Types of

Matrices, no. of

layers

The inorganic matrix system was

effective in increasing the strength

and stiffness of the RC beams, but the

failure mechanism of the inorganic

system seemed more brittle

11 Kurtz and Balaguru

(2001)

Types of

Matrices

The inorganic matrix and the organic

matrix were equally effective at

increasing the strength and stiffness

of the beams, although the inorganic

matrix slightly reduced ductility

Spadea et al. (2001) CFRP layouts Externally bonding a CFRP plate to

strengthen the RC beams increased

the flexural strength but reduced

ductility

Rasheed and Pervaiz

(2003) and Spadea et

al. (1998)

Shear modulus

and thickness of

Adhesiv3e

The FRP tension force cannot be

fully developed when the adhesive

shear modulus is below 65 MPa/mm

(239 ksi/in.) of the adhesive layer

thickness regardless of the length of

the plate

Brena et al. (2003) Layout of

CFRP

The use of CFRP U-wraps delayed or

prevented the CFRP composite

sheets from debonding

Alagusundaramoorthy

et al. (2003)

Type of FRP,

anchorage

The increase in strength was 49% and

40% for beams strengthened with

CFRP sheet and fabric, respectively.

A 58% increase was achieved when

anchorages were used.

12 Akbarzadeh and

Maghsoudi (2011)

Effect of hybrid

FRP

Using HCG to strengthen the

continuous RC beams led to

considerable increases in the bearing

capacity

13 Attari et al. (2012) Effect of hybrid

FRP

The cost-effectiveness of using twin

layers of glass–carbon FRP fabric as

a strengthening configuration for RC

structures

Rami et al. (2014) Effect of hybrid

FRP

The ductility at failure loads of the

beams strengthened with glass and

hybrid sheets is higher than that with

a single carbon sheet

15

Figure 2.1 : Strengthened RC beams tested by Attari et al. (2012)

2.2.2 Limitations of EBR System

The use of CFRP sheets or strips without appropriate anchorage severely decreases

structural ductility and causes early debonding of the CFRP laminate. The strengthened

member cannot reach the theoretical ultimate strength calculated by assuming a perfect

bond between the laminate and concrete. By anchoring CFRP laminates using bolts and

steel plates for end anchorage, and steel or FRP straps along the beam, the composite

action of the strengthened beam can be maintained up to its ultimate load. However, for

a span to depth ratio greater than 4.0, anchorage had no effect on the peeling-off of the

laminate.

Figure 2.2. Different failure modes of EBR system

Concrete beam

Load cell

16

Ten failure modes are theoretically possible in RC beams externally strengthened with

either steel or FRP materials. The first nine failure modes are as shown in Figure 2.2 (the

number in parenthesis indicate type of failure mode in Figure 2.2) and names of ten failure

modes are given below:

i. Rupture of the strengthening plate (1),

ii. Rupture of the internal reinforcement (2),

iii. Crushing of concrete in the compression zone (3),

iv. Shear failure (4),

v. Failure caused by debonding (peeling-off) (5),

vi. Rupture of the strengthening-adhesive interface (6),

vii. Rupture of the concrete-adhesive interface (7),

viii. Cohesive failure within the adhesive (8),

ix. Interlaminate shear failure within the CFRP material (observed as a

secondary failure) (9), and

x. Concrete cover peeling off.

For steel plated RC beams, the ultimate failure mode appears to be closely related to

the geometry of the plated cross-section. Thin plates usually fail in flexural. However,

when the plate aspect ratio falls below a certain value, separation of the plate from the

beam can occur. This usually starts from the plate end and results in the concrete cover

being ripped off. These observations are consistent with the fact that simple elastic

longitudinal shear stresses are inversely proportional to plate width. Therefore, as the steel

plate width decreases, the longitudinal shear stresses increase. The bending stiffness of

the plate also increases, and thereby increases the peeling stresses normal to the beam.

17

Shear and normal stresses become concentrated at the plate ends of strengthened

beams subjected to flexure. This is caused by incompatibility between the plate stiffness

and the concrete stiffness. This incompatibility can only be overcome by severe distortion

of the adhesive layer. The transition area from the basic member to the plate

reinforcement is a region of high shear and low bending moment. The changing bending

moment and distortion in the adhesive layer causes a build-up of axial forces at the ends

of the external plate. This leads to high bond stresses in the adhesive to plate and adhesive

to concrete interfaces, which may reach critical levels and thereby cause failure. The

magnitude of these plate end stresses depends upon a number of factors. These factors

are: the geometry of the plate reinforcement, the engineering properties of the adhesive

and the shear strength of the original concrete beam (Swamy & Mukhopadhyaya, 1995).

The peak peeling and shear stresses at the plate ends, in addition to bending stresses,

result in a biaxial tensile stress state. This causes the cracks initiated at the plate ends to

extend horizontally at the level of the internal steel reinforcement.

When failure occurs in delamination, the use of a more flexible adhesive is

advantageous, since the area over which the tensile strain builds up in the external steel

plate is increased. This results in a lower peak stress. Jones et al. (1988) verified this

procedure experimentally. Beams strengthened using an adhesive with an elastic modulus

of around 1.0x103 N/mm2 gave slightly improved strengths when failure occurred by plate

separation than strengths given by an adhesive with a modulus of around 10x103 N/mm2.

Many models have been developed and proposed in the past to predict plate end

debonding failure load. However, no existing model can accurately predict the failure

load when cover failure occurs (Smith and Teng, 2002). In addition, they could not

consider and distinguish end delamination and concrete cover separation.

18

2.2.3 Eliminating Premature Debonding in EBR

To avoid peeling failures several approaches have been investigated and developed.

Some of these include mechanical anchorages at the ends of the sheet, wrapped sheets

around the web of the beam over the longitudinal FRP sheet, and changes in the geometry

of the sheets in the anchorage zones as suggested by Karam (1992).

Swamy et al. (1987a) showed that premature debonding of steel plates can effectively

be avoided by ensuring that the width to thickness ratio of the plate is not less than 50.

Swamy and Mukopadhyaya (1995) have shown that this recommendation holds true for

FRP plates when glass, glass-carbon, and aramid fibers are used. In the case of CFRP, the

plates are generally so thin that this criterion is automatically satisfied. Another technique

that can be used if multiple layers are being prestressed is to end the layers (and transfer

the prestress) at different locations along the beam. This technique is effective at reducing

the magnitude of shear and normal stress concentrations that occur at the plate ends

(Wight, 1998).

By using bonded angle plates or transverse FRP wraps, longitudinal FRP strips can be

effectively anchored to the tensile face of the beam. The effectiveness of this technique

has been commented on by Adimi et al. (2000), who found that a great deal of ductility

could be observed until rupture of the plate, shear failure of the wrap, or angle plates.

Jones et al. (1988) mentioned that the bonded anchor plates were more effective,

producing yielding of the tensile plates and allowing the full theoretical strength to be

achieved, 36% above that of the unplated control beam. The anchorage detail was also

found to affect the ductility of the beams near the ultimate load. Unanchored, the beams

failed suddenly with little or no ductility. The beams with bolts or anchor plates all had

similar ductility’s, at least as high as the unplated control.

19

Deblois et al. (1992) compared bonded unidirectional and bidirectional GFRP sheets

with bolted unidirectional GFRP sheets using 1.0 m and 4.1 m specimens. They found

that bolted sheets and bidirectional sheets were more effective than unbolted

unidirectional sheets.

Sharif et al. (1994) studied three different anchorage schemes for GFRP plates using

small-scale beams. The three schemes were bolting the plates to the tension face, bolting

combined with FRP plates bonded to the sides of the beams, and a special one-piece I-

jacket plate that was glued along the bottom of the whole span to the sides of the beam in

the shear span. The I-jacket was the most effective anchorage scheme as it prevented all

types of peeling failures. Bolting the plates was not very effective as the beams failed by

shear peeling.

Hussain et al. (1995) tried anchor bolts. The percentage improvement in ductility due

to the addition of bolts was found to decrease as plate thickness increased. The end

anchorage could not prevent premature failure of the beams, although in this case failure

occurred as a result of diagonal shear cracks in the shear spans. Providing anchorage to

steel plated beams involves considerable extra site work and this increases the cost of

EBR considerably. However, in the case of steel EBR, the use of anchorage is completely

necessary.

The University of Surrey (Quantrill et al., 1996) under the ROBUST programme of

research, conducted a parametric study on RC beams flexurally strengthened with GFRP

bonded plates. The study varied a number of parameters. These were the concrete

strength, the pultruded composite plate area and its aspect ratio. As mentioned above,

thick narrow plates that have an aspect ratio of less than 50 have been linked with brittle

peeling failure modes. Thus, this study tested plates with aspect ratios of 38 and 67. The

effect of the width to thickness ratio was isolated in these tests by keeping the plate cross-

20

sectional area constant. The tests found that plating considerably enhances both the

strength and stiffness of RC members, although this is at the expense of ductility at failure.

The study also observed that higher strength concrete produced the greatest increase in

strength over unplated sections and that the aspect ratio of the plates had little effect on

the overall behaviour of the beams.

The ROBUST programme conducted further investigations at the University of Surrey

(Quantrill et al., 1996) on the experimental and analytical strengthening of RC beams

with FRP plates. They analyzed the effects of different plate parameters on the overall

behaviour of the strengthening system. The study showed that relatively small scale 1 m

long specimens can be tested to reveal useful information on the behaviour of

strengthened beams. Reducing the plate area led to an expected reduction in strengthening

and stiffening, which caused the ductility and the plate strains for a given load to increase.

The aspect ratio for the values tested had little effect on the overall behaviour of the

beams. Using CFRP plates increased the serviceability, yield and ultimate loads and

increased the stiffness of the strengthened members after both cracking and yielding. The

ductility of the strengthened beams was reduced. For a partially cracked section, the

tensile plate strain and compressive concrete strain responses of the beam were accurately

predicted by the iterative analytical model.

Garden and Hollaway (1998) tested concrete beams strengthened with CFRP plates to

study the effects of three parameters: plate aspect ratio (plate width divided by plate

thickness) at constant cross sectional area; shear span-depth ratio of beams; and the form

of plate end anchorage. The plates were anchored by extending them under the supports,

or attaching them to GFRP angles bonded to the sides of the beams. The ultimate

capacities of the strengthened beams decreased with reducing plate width–thickness

ratios. Failure was always accompanied by concrete cover separation from internal

21

reinforcement. Increasing the shear span-depth ratios resulted in improved ultimate

capacities. Anchoring the sheets increased the strength of the beams.

Spadea et al. (1998) and Gemert (1999) also found that wrapping the sides of the

beams with vertical FRP sheets provided effective anchorage for the flexural sheets.

Quantrill et al. (1996) found that GFRP angles attached to the sides of the beams were

effective anchors. On the other hand, Naaman (1999) tested 3 m span T-beams and did

not find any improvement in the strength of the beams when U-shaped anchors were used.

Teng et al. (1999) conducted an experimental study into strengthening deficient

cantilever concrete slabs by bonding GFRP strips on the top surface. Different anchorage

systems were used, and the most effective method was to anchor the GFRP strips into the

walls through horizontal slots and into the slab with fiber anchors. This method allowed

the full strength of the strips to develop, and the strength was almost four times that of

the unstrengthened beam.

Bencardino et al. (2007) tested CFRP plated beams and recorded the reduction in

member ductility due to plating without end anchorage. The ductility of the strengthened

beams was restored when anchorage in the form of externally bonded U-shaped steel

stirrups was fitted on to the plated beams. The study then successfully used this method

of CFRP plating to strengthen an experimental portal structure.

Xiong et al. (2007) attempted to strengthen RC beams by combining unidirectional

CFRP sheets (to bond to the tension faces of the beams) and bi-directional GFRP sheets

(to wrap three sides of the beams continuously). The feasibility and potential advantages

of this approach were discussed. A comparative test program using ten beams was carried

out. The test results showed that the hybrid CFRP and GFRP (H-CF/GF-RP)

strengthening not only prevented the tension delamination of the bottom concrete cover,

22

but also lead to a significant increase in the deformation capacity of the strengthened

beams at a very low cost compared to CFRP strengthening alone.

Galal and Mofidi (2009) explored a new hybrid FRP sheet and ductile anchor system

for the rehabilitation of RC beams. The study reports that the advantage of this

strengthening method is that it overcomes the problem of low ductility that is connected

to the brittle failure of beams conventionally strengthened using epoxy bonded FRP

sheets. The proposed system leads to a ductile failure mode by triggering yielding to occur

in a steel anchor system (steel links) rather than by rupture or debonding of the FRP

sheets, which is sudden in nature. Four half-scale RC T-beams were tested under four-

point loading. Three retrofitted beams were strengthened using one layer of a CFRP sheet.

The behaviour of the two beams that were strengthened with the new hybrid FRP sheet

and ductile anchor system were compared with the behaviour of the beam conventionally

strengthened with epoxy bonded FRP sheet and the control beam. The results showed that

the proposed strengthening system effectively increased flexural capacity and ductility of

RC beams.

Zhou et al. (2013) developed and investigated a new FRP bonding system, the friction

hybrid bonded FRP (FHB-FRP) technique, in which they use new mechanical fasteners.

Debonding of FRP plates can be effectively prevented with the use of the FHB-FRP

strengthening system. Compared to the use of U-jackets, strengthening beams using the

FHB-FRP technique can increase the utilization of the tensile capacity of FRP. RC beams

strengthened with the FHB-FRP technique had higher yielding loads and lower yielding

load ratios than beams strengthened using the U-jacketing technique. Thus, the FHB

technique can provide strengthened beams with a higher service load-carrying capacity.

23

2.2.4 Near Surface Mounting (NSM) Technique

The NSM reinforcement technique involves making a groove in the surface of the

member, roughening and cleaning the groove, filling the groove halfway with a structural

adhesive, installing the reinforcing bar or laminate, filling the groove completely with

structural adhesive, and leveling the surface. NSM FRP bars and laminates are

increasingly being applied as a substitute to externally bonded FRP laminates. The NSM

FRP technique may be especially suitable for cases in which the concrete surface is very

rough, weak, or requires significant surface preparation.

Lorenzis et al. (2000) and Lorenzis and Nanni (2002) conducted research on NSM

techniques with FRP to strengthen various types of beams. The study investigated both

flexural and shear strengthening. The study found that end debonding of FRP bars was

the dominant failure mode for T-beams and rectangular beams with low reinforcement

ratios. Rectangular beams with greater reinforcement ratios failed by concrete crushing.

The researchers proposed a system for post-tensioning the NSM system in cases where

the ends of the beam were not accessible. Their test results demonstrated that for the

flexurally strengthened RC beams, the ultimate strength increased by 44% as compared

to the control beam.

Hassan and Rizkalla (2003) investigated the different strengthening systems as well as

different types of FRP for the strengthening of large scale prestressed concrete beams.

The test results confirmed that the application of NSM FRP was feasible and cost-

effective for strengthening concrete bridge members.

Yost et al. (2004) studied the structural performance of retrofitted concrete flexural

members using the NSM CFRP method. They reported an increase of 30% and 78% in

the yield load and ultimate strength, respectively when compared to the control beam.

They also found that the bonds between the CFRP reinforcement, the epoxy and the

24

adjacent concrete were strong enough to develop the full tensile capacity of the CFRP

reinforcement.

El-Hacha et al. (2004) investigated the feasibility of using NSM CFRP to strengthen

RC beams. The study found that complete composite action between the NSM strips and

the concrete was achieved. The flexural capacity of the strengthened RC beams likewise

increased.

El-Hacha and Rizkalla (2004b)also conducted a study on the flexural strengthening of

RC beams using the NSM FRP technique. The variables examined were the number of

FRP bars or strips, the form of FRP – (either strips or bars) and the type of FRP – (either

glass or carbon). They found that using NSM reinforcement with CFRP strips for flexural

strengthening resulted in beams that had a higher load carrying capacity than those

strengthened with CFRP bars with the same axial stiffness. The results were explained as

possibly being due to debonding occurring earlier between the CFRP bar and the epoxy

interface.

Rosenboom et al. (2004) strengthened twelve pre-stressed concrete girders with

various CFRP systems and tested them under static and fatigue loading. The girders

strengthened with NSM CFRP bars and strips achieved a 20% increase in ultimate

flexural capacity compared with the control girder when monotonically loaded to failure.

The NSM-strengthened girders also performed well under fatigue loading conditions,

surviving over two million cycles of increased service loading with little degradation and

reduced crack widths.

Barros and Fortes (2005) and Barros et al. (2006) investigated the effectiveness of

using CFRP laminates as NSM reinforcement for structural strengthening. The different

variables examined were the number of CFRP laminates, different steel reinforcement

25

ratios, and different depths of the cross-section. An average improvement of 91% on the

ultimate load was obtained. The study also found that high ductility at failure of the

strengthened RC beams was assured. A serviceability limit state analysis showed an

increase in the rigidity of the beam by 28%.

Jung et al. (2006) performed an experimental investigation on the flexural behaviour

of RC beams strengthened with NSM CFRP reinforcement. They compared the NSM

CFRP strengthened beams to beams strengthened using externally bonded CFRP. The

NSM strengthened specimens utilized the CFRP reinforcement more efficiently than the

externally strengthened beams.

An analytical evaluation of RC beams strengthened with NSM strips was presented by

Kang et al. (2006). The study focused on the relation between the ultimate strength of the

beam and the depth of the NSM groove and the spacing between the CFRP strips. They

concluded that the minimum spacing between the NSM groove (for multiple CFRP strips)

and the edge of the beam should be more than 40 mm to ensure that each CFRP strip

behaved independently.

Aidoo et al. (2006) made a full-scale experimental investigation on the repairing of an

RC interstate bridge using CFRP material. The three types of strengthening methods

investigated were: externally bonded reinforcement, NSM reinforcement, and powder

actuated fasteners. All three methods improved the load-carrying capacity of the girders.

In particular, the externally bonded CFRP and NSM CFRP behaved better than the

powder actuated fasteners. However, the NSM reinforcement showed a significantly

higher ductility and this was explained as being due to the better bond characteristics.

Soliman et al. (2010) investigated the behaviour of twenty RC beams flexurally

strengthened with NSM FRP bars. Different variables including internal steel ratio, type

26

and diameter of FRP bars, contact length and groove dimension were investigated in their

research. Test results confirmed that the application of NSM FRP bars was effective in

improving the flexural capacity of the concrete beams.

Figure 2.3: EBROG technique (Mostofinejad & Shameli, 2013)

Mostofinejad and Shameli (2013) investigated two new methods named as externally

bonded reinforcement on grooves (EBROG) shown in Figure 2.3 and externally bonded

reinforcement in grooves (EBRIG) as alternative to conventional externally bonded

reinforcement (EBR). Results showed considerable increase in ultimate limits for beams

strengthened with EBROG and EBRIG techniques as compared to those strengthened

with the EBR method.

27

Figure 2.4: Failure modes of beams strengthened with NSM CFRP bars

(Sharaky et al., 2014)

Sharaky et al. (2014) investigated eight beams to study the behaviour of RC beams

strengthened with NSM FRP bars under four-point bending. The effects of material type,

epoxy properties, bar size and the number of NSM bars were studied. They found that

increasing the number increased the yielding and the maximum loads. However, the small

percentage increment in the maximum load was mainly due to the concrete cover

separation mode of failure as shown in Figure 2.4.

Bilotta et al. (2015) conducted flexural tests on RC beams strengthened with both NSM

and EBR techniques. The results showed that the debonding phenomena for NSM strip

strengthened beams are less significant than for EBR plate beams. Moreover, the effect

of the loading pattern was analyzed to evaluate the sensitivity of failure modes and loads

to different distributions of bending moment and shear along the beam.

28

2.2.5 Limitations of NSM Technique

Although end debonding failures are less likely in NSM FRP compared to EBR-FRP,

they may still notably limit the application of this technology. The debonding failure

depends on several factors, like the internal steel reinforcement ratio, the FRP

reinforcement ratio, the cross-section and surface condition of the NSM reinforcement,

and the strengths of both the epoxy and the concrete. Some researchers (Lorenzis, 2002;

Taljsten et al., 2003) extended the NSM FRP over the beam supports to provide anchorage

in adjacent members. In spite of this anchorage, debonding can still occur (Lorenzis,

2002). However, Taljsten et al. (2003) reported that one beam failed by FRP rupture

where the reinforcement was extended over the supports, as opposed to the failure by

debonding observed in an identical beam where the NSM reinforcement did not extend

over the supports. Blaschko and Zilch (1999) reported the results of tests on two beams

strengthened with NSM FRP. The first beam failed by end debonding from the cut-off

section but the second beam with a steel U-jacket bonded to the cut-off section, failed by

FRP rapture.

29

Figure 2.5: Failure mode of the NSM technique (Lorenzis & Teng, 2007)

De Lorenzis and Teng (2007) observed seven debonding failure modes for RC beams

flexurally-strengthened with NSM bars and strips. These seven modes are shown in

30

Figure 2.5 and described (the alphabet in parenthesis indicate the type of failure in Figure

2.5) below:

i. Separation at the bar-epoxy interface (a),

ii. Concrete cover separation between two cracks in the maximum

moment region (b),

iii. Concrete cover separation over a large length of the beam (c),

iv. Concrete cover separation starting from a cutoff section (d),

v. Concrete cover separation along the edge (e),

vi. Secondary failure of bond between epoxy and concrete (f), and

vii. Secondary splitting of the epoxy (g).

The mechanics of end debonding in beams strengthened with the NSM technique is

still not fully understood. Descriptions of modes of failure in available literature are often

not sufficiently detailed enough to provide an understanding of the progression of the

failure. Based on the available experimental data in research works, the probable failure

modes of beams strengthened with NSM FRP reinforcement are shown in Figure 2.5. The

interaction between the primary failure modes and the secondary failure modes are not

still clear and require further investigation.

De Lorenzis and Teng (2007) have pointed out that a large number of factors can affect

the flexural behaviour of RC beams with NSM FRP, and thus further experimental and

theoretical study is required, particularly to clarify the debonding failure mechanisms in

the NSM reinforced beam. Also, the interaction between concrete cover separation and

other modes of failure that occur to the NSM FRP concrete interface, such as fracture at

the epoxy and concrete interface and separation of the epoxy cover, needs further

research. Additionally, investigating the behaviour of pre-damaged beams strengthened

31

with NSM FRP would be significant especially in the practical field, as cracking and

damage to the concrete cover may have a significant influence on the debonding failure

process. Lorenzis and Teng (2007) have also recommended that the relationship between

bond failure mechanisms and debonding failure mechanisms in flexurally-strengthened

beams can be clarified through detailed experimentation and theoretical modeling. In such

an investigation, the interaction between flexural or flexural-shear cracking and bond

stresses must be clarified for the development of numerical and analytical models to

predict debonding failure.

2.2.6 Fatigue Performance of EBR and NSM Technique

2.2.6.1 Strengthened with Steel

A limited number of experimental investigations into the fatigue performance of RC

beams rehabilitated with externally bonded steel plates have been reported. Iyer et al.

(1989) found that steel plating was not greatly affected by cyclic loading. It can be

assumed that the steel plates were able to forestall fatigue failure in the internal

reinforcing steel by attracting a portion of the internal tensile stress in the beam and, thus,

reduce the stress range applied to the internal reinforcement.

Byung et al. (2003) investigated the static and fatigue behaviour of RC beams

strengthened with steel plates. A comprehensive test program was set up and series of

strengthened beams were tested. Their study found that the strengthened beams exhibited

much higher fatigue resistance than the unstrengthened beams at the same fatigue load

level. The increase in deflections of the strengthened beams according to the number of

load cycles was much smaller than that of the unstrengthened beams. After applying

43106 cycles under 60% and 70% fatigue load levels, the beams were tested up to failure.

The ultimate fatigue loads were found to be similar to the static failure load. This indicates

32

that a fatigue load below 70% of the static failure load does not decrease the ultimate

strength of strengthened beams.

2.2.6.2 Strengthened with FRP

Kaiser (1989) conducted fatigue tests at EMPA on RC beams strengthened with a glass

and carbon fiber hybrid composite. The cross-section of the RC beam was 300 mm wide

and 250 mm deep, and the span was 2000 mm. The conventional reinforcement consisted

of two 8 mm rebars in the tension zone. The composite sheet had a 0.3 mm by 200 mm

cross-section and was bonded to the tensile face of the beam. The beam was subjected to

two-point loading and cycled from 1 kN to 19 kN (0.2 kips to 4.3 kips) at a frequency of

4 Hz, corresponding to a stress range in the reinforcing bars of 386 N/mm (56 ksi). The

first fatigue damage to the rebars occurred after 480,000 cycles. The first damage in the

composite appeared after 750,000 cycles in the form of fracturing of individual fibers in

the strips. The relatively sharp concrete at the edges of cracks rubbed against the strips at

every cycle, and the composite finally failed after 805,000 cycles. These results clearly

indicate that FRP laminates can sustain significant loading after failure of the steel

reinforcement.

Fatigue tests by Shijie and Ruixian (1993) showed that the fatigue lives of GFRP plated

members could be up to three times longer than the life of an unstrengthened RC control

specimen. The fatigue strength could be increased from 15% to 30% and mid-span

deflection could be reduced to 40%. The bending capabilities of the reinforced beam

diminished with the increasing number of cycles. For example, the static loading test for

one beam showed that after 2x1010 cycles the limiting bending moment of the mid-span

location diminished from 244.3 kN-m to 198.4 kN-m. Both the post-cyclic static strength

and stiffness diminished as number of cycles increased, but by a smaller magnitude than

for the unstrengthened beam.

33

Meier (1995) performed further tests at EMPA on beams with T-shaped cross-sections

under more realistic loading conditions. The cross-section was 900 mm wide and 500 mm

deep, and the span was 6000 mm. The beams were tested under cyclic loading ranging

from 126 kN to 283 kN, representing 15% to 35% of the static ultimate capacity of the

beams. The corresponding stress range in the rebars was 131 N/mm. Crack development

was noted after 2 million cycles. After 10.7 million cycles at room temperature, the test

temperature was increased to 40°C and the relative humidity to 95%. The first failure in

the rebars occurred at 12 million cycles. After 14.09 million cycles, the second bar failed

and the CFRP strip sheared from the concrete surface. A third fatigue test similar to the

one described above was conducted at EMPA with pre-tensioned strips, and 30 million

load cycles were performed without any damage.

Inoue (1996) investigated the strengthening of RC beams by adhesion of CFRP plates.

The beams were tested under static and fatigue loading for strength and deformation

characteristics. The study compared RC beams strengthened with CFRP plates bonded to

the underside of the beam with resin adhesive and RC beams where the CFRP plates were

fixed with anchor bolts as well as resin adhesive. The results of the study indicate that the

appropriate fatigue life of the CFRP beams can be estimated from the reinforcement

stress, which in turn can be determined on the basis of linear elastic theory by assuming

a crack section and the S-N equation of the reinforcement in JSCE’s specifications. The

installation of an anchor bolt increases the fatigue life of strengthened beams under high

loads but it exerts little effect on the static strength.

Barnes and Mays (1999) investigated the fatigue performance of RC beams

strengthened using CFRP plates for design applications. Five RC beam specimens, 2300

mm long, 130 mm wide, and 230 mm in depth, were tested. Two beams were unplated

34

control specimens, and three were plated beams. The strengthening plates consisted of

68% volume fraction high-strength unidirectional carbon fibers (Toray T300) embedded

in a vinyl ester resin, and bonded using a two-part cold-curing epoxy adhesive (Sikadur

31 PBA). Each specimen was subjected to two-point loading at a frequency of 1 Hz. Three

loading options were tested as follows:

i. Apply the same load to both the plated and unplated beams,

ii. Apply loads to give the same stress range in the rebars of both beams, and

iii. Apply the same percentage of ultimate static capacity to each specimen.

The study found that the plated beams demonstrated better stress endurance

performance. However, the authors concluded that a criterion for design guidance would

be to expect the same fatigue life for plated and unplated beams, with similar ranges of

stress in the reinforcing steel (Asplund, 1949).

Shahawy and Beitelman (1999) performed fatigue tests on severely cracked RC beams

post-strengthened using different arrangements of CFRP biaxial fabrics applied on the

bottom face or fully wrapped on the stem. The objective of the tests was to study the

effect of strengthening on the extension of fatigue life of severely damaged members.

They tested six beams with T-shaped cross-sections that were 584 mm wide, 445 mm

high, and with a 5790 mm span. The beams were loaded at two points. The loads

represented 25% to 50% of the ultimate capacity, with the stress range in the rebars being

about 103.4 MPa. At this level, the authors expected the steel to have a fatigue life of

approximately one million cycles. The unstrengthened control specimen failed after

295,000 cycles. One unstrengthened specimen was previously subjected to fatigue

loading for 150,000 cycles and then strengthened using two layers of CFRP biaxial fabric

bonded on the full stem of the beam. This specimen failed after two million cycles

following rupture of the fabric, after fatigue failure of the internal steel. After

35

strengthening, the specimen demonstrated a slight increase in stiffness up to the time just

before failure. Specimens wrapped with three layers of fabric survived up to 3 million

cycles. The researchers concluded that the fatigue life of strengthened specimens was

prolonged and that severely damaged members could be effectively rehabilitated using

externally bonded CFRP materials.

Benouaich (2000) tested six specimens, strengthened using different configurations of

CFRP flexible sheets and pultruded plates. The beams were subjected to fatigue loading

under various stress ranges representative of service-load conditions and potential

overloading. Test results showed no evidence of damage propagation at the concrete-

composite interface when beams were subjected to service-load cycling. Monotonic tests

demonstrated no influence of the fatigue loading on the ultimate static capacity. However,

post-cyclic ultimate deformations and structural ductility were reduced after cyclic

loading. Fatigue performance under high stress ranges appeared to be governed by

debonding at the concrete-adhesive interface.

Papakonstantinou et al. (2001) examined the effects of GFRP composite rehabilitation

systems on the fatigue performance of RC beams. The results of their study indicated that

the fatigue life of RC beams, for a given geometry and subjected to similar cyclic loading,

can be significantly extended through the use of externally bonded GFRP composite

sheets.

Deng (2002) investigated the static and fatigue behaviour of RC beams strengthened

with CFRP sheets bonded with organic and inorganic matrices. The study examined the

crack behaviour, failure mode, strength improvement/behaviour, stiffness behaviour,

strain behaviour and fatigue life behaviour of the strengthened beams. The results showed

that the RC beams bonded with organic matrices and those bonded with inorganic

36

matrices behaved differently. They study also found that the fatigue lives of RC beams

strengthened with CFRP exhibited Weibull probability distribution.

Aidoo et al. (2004) examined the flexural fatigue performance of RC bridge girders

strengthened with one-dimensional FRP composites. The study used eight RC T-beams,

508 mm deep and 5.6 m long, with and without bonded FRP reinforcement on their tensile

surfaces. The beams were tested with concentrated loads at mid-span under constant

amplitude cyclic loading. The results of the study indicated that the fatigue behaviour of

beams strengthened with one-dimensional FRP composites is controlled by the fatigue

behaviour of the reinforcing steel and that the fatigue life of RC beams can be increased

by the application of FRP composites, which relieve some of the stress carried by the

steel.

Heffernan and Erki (2004) investigated the fatigue behaviour of RC beams post-

strengthened with CFRP laminates. They tested twenty 3 m and six 5 m beams loaded

monotonically and cyclically to failure, comparing beams with and without CFRP

strengthening. They also examined the effect on fatigue life on increasing the amount of

CFRP used to strengthen beams. The study found that the use of CFRP sheets lowered

stresses in the tensile steel. Thus, the fatigue life of all the beams, without and with CFRP

strengthening, was directly related to the fatigue characteristics of the tensile reinforcing

steel and its stress history due to the applied loading. Concrete softening due to repeated

loads caused an increase in the stresses in the tensile steel. The CFRP strengthened beams

had less severe increases in steel stresses than the beams without CFRP sheets. There was

no significant degradation due to cyclic loading in the CFRP sheets or the CFRP to

concrete interface. Thus, the basic assumptions for monotonic behaviour remained valid

for the beams loaded cyclically.

37

Gussenhoven and Brena (2005) tested thirteen small-scale beams strengthened using

CFRP composites. The beams were tested under repeated loads to investigate their fatigue

behaviour. Test results indicated that peak-stress applied to the reinforcing steel in

combination with composite laminate configuration were the main parameters that

affected the controlling failure mode.

Brena et al. (2005) conducted an experimental program that consisted of fatigue testing

of ten RC beams strengthened using two different types of externally bonded CFRP

composites. The results indicated that the bond between the composite laminates and the

surface of the concrete can degrade at load amplitudes corresponding to extreme load

conditions for a bridge. These results showed that an upper limit on stresses generated

along the composite-concrete interface might have to be set during the design stage to

avoid premature debonding after a limited number of load cycles.

Ekenel et al. (2006) examined the flexural strength of RC beams using two FRP

strengthening systems. Two of the RC beams were maintained as unstrengthened control

specimens. Three beams were strengthened using CFRP fabrics. The two remaining

beams were strengthened with FRP pre-cured laminates. One of the beams strengthened

with CFRP fabric also used glass fiber anchor spikes. Of the two beams strengthened with

FRP pre-cured laminates, one was bonded using epoxy adhesive and the other one was

attached with mechanical fasteners. Five beams were tested under fatigue loading for two

million cycles and all five beams survived. The results showed that use of anchor spikes

in fabric strengthening increases ultimate strength, and mechanical fasteners can be an

alternative to epoxy bonding in pre-cured laminate systems.

Toutanji et al. (2006) studied the fatigue performance of concrete beams strengthened

with CFRP sheets bonded with an inorganic matrix. Large scale RC beams were

strengthened with three layers of CFRP sheets and tested under fatigue loading. The

38

relationships between fatigue strength, crack width, and number of cycles were studied

and analyzed. The results showed that both the load capacity of the RC beams and the

number of cycles the RC beams could withstand were significantly increased with CFRP

sheets.

Ferrier et al. (2011) focused on the damage behaviour of FRP strengthened RC

structures subjected to fatigue loading in their study. They developed a model calibrated

using data from existing literature and from experimental investigations specifically

carried out for the study. The model was able to correctly estimate the fatigue behaviour

of FRP strengthened beams, as deflection and strain in the different materials could be

calculated with a sufficient accuracy.

Al-Rousan and Issa (2011) carried out an experimental and analytical to study the

performance of nine RC beams externally strengthened with various configurations of

CFRP sheets. The beams were subjected to static and accelerated fatigue testing. The

beams were tested for various stress ranges. After validating a non-linear finite element

analysis (NLFEA) with experimental test results, the analysis was extended to provide a

better understanding of the effect of: fatigue stress ranges, the number of CFRP layers,

and the CFRP to concrete contact area on the performance of RC beams. Stress ranges

were found to have a significant effect on the permanent deflection at mid-span especially

for higher stress ranges. Cyclic fatigue loading produced a time-dependent redistribution

of the stresses, which led to a sudden drop in concrete stresses and a mild increase in steel

and CFRP sheet stresses as fatigue life was exhausted.

Regarding the NSM technique, Quattlebaum et al. (2005) evaluated the static and

fatigue performance of reinforced concrete beams retrofitted with conventional adhesive

applied (CAA), NSM, and powder actuated fastener-applied (PAF) FRP retrofit systems.

39

The results of this study indicate that the CAA method is outperformed by the other

methods under cyclic conditions.

Badawi (2007) studied RC beams with non pre-stressed and pre-stressed CFRP bars

to increase the static and fatigue strength of the beams. The test results showed that RC

beams strengthened with NSM CFRP bars increased both the static capacity and the

fatigue strength.

Yost et al. (2007) studied how fatigue loading for 2,000,000 cycles affected the static

performance and stiffness of simply supported steel reinforced beams with NSM FRP

bars and strips. Test results showed that all beams strengthened with CFRP plates and

CFRP bars survived the 2,000,000 cycles with no significant loss in bond or force transfer.

Thus, composite action between concrete and the NSM CFRP appears to be unaffected

by fatigue loading

Oudah and El-Hacha (2012) studied the fatigue behaviour of RC beams strengthened

using pre-stressed NSM-FRP strips. Experimental test results show that the deflection

increase at the end of fatigue loading was almost similar for all beams, which indicates

that damage accumulation is not dependent from the pre-stress level.

Wahab et al. (2012) tested ten concrete beams strengthened with NSM pre-stressed

FRP bars under different fatigue load levels. The test variables included the type of CFRP

rod (spirally wound or sand-coated) and the fatigue load level. Test results showed that

the sand-coated rods exhibited a better bond fatigue performance than the spirally wound

rods, whereas at a given load level, the beams strengthened with sand-coated rods had

longer fatigue lives than the beams strengthened with spirally wound rods. Also, for a

given number of cycles, the beams strengthened with prestressed CFRP rods failed in

40

bond at a lower applied load range than the beams strengthened with a non pre-stressed

CFRP rod.

2.3 Numerical Modelling

A number of research works on numerical analysis have been done to predict the

failure mechanism and interfacial stress of strengthened RC beams. Adhikary and

Mutsuyoshi (2002), in their modelling of RC beams, took into account the slip effect

between the concrete and the strengthening steel plates, and the non-linear behaviour of

concrete, reinforcing bars and steel plates. Wolanski (2004) studied flexural behaviour of

reinforced and pre-stressed concrete beams using finite element analysis.

Kachlakev and Miller (2001) studied “Finite Element Modeling of RC Structures

Strengthened with FRP Laminates” with ANSYS and the objectives of this modeling was

to investigate the structural performance of Horsetail Creek Bridge (which is a historic

bridge, built in 1914).

Zhang and Teng (2010) predicted the interfacial stresses using the finite element

method. Five different finite element modeling approaches based on different

assumptions for the deformations of the three components of such a plated beam (i.e.

beam, adhesive layer and plate) are described. These results provide a useful insight into

the risk of debonding in such plated panels.

Al-Rousan and Issa (2011) validated a non-linear finite element analysis (NLFEA)

with experimental test results, the analysis was extended to provide a better understanding

of the effect of: fatigue stress ranges, the number of CFRP layers, and the CFRP to

concrete contact area on the performance of RC beams. Stress ranges were found to have

41

a significant effect on the permanent deflection at mid-span especially for higher stress

ranges.

Radfar et al. (2012) carried out a non-linear finite element analysis using the

commercial program ABAQUS to predict ultimate loading capacity and the failure mode

of RC beams in a four-point bending setup. A series of 4 RC beams strengthened with

FRP sheets at the bottom were tested to failure under a four-point bending load. By

comparing numerical results with experimental ones, the proposed finite element model

has been validated and can be used for further prediction of this type of failure.

Hawileh (2012) develop a detailed 3D nonlinear FEM that can accurately predicts the

load-carrying capacity and response of RC beams strengthened with NSM FRP rods

subjected to four-point bending loading using the finite element code, ANSYS. The

developed FE models have been validated by comparing the predicted failure mode and

mid-span deflection with that of the measured experimental data obtained by Al-

Mahmoud et al. (2009). In addition, the validated FEM are used to study the effect of

NSM bar material types and CFRP rod diameter on the global response of the

strengthened RC beams. The results of this study showed the practicality and validity of

the finite element method in modeling RC beams strengthened in flexure using NSM

CFRP bar reinforcement.

Omran and El-Hacha (2012) developed a comprehensive 3D nonlinear Finite Element

(FE) analysis of Reinforced Concrete (RC) beams strengthened with prestressed NSM-

CFRP strips. Debonding effect at the epoxy-concrete interface was considered in the

model by identification of fracture energies of the interfaces and appropriate bilinear

shear stress-slip and tension stress-gap models. Prestressing was applied to the CFRP

strips by adopting the equivalent temperature method.

42

Zhang and Teng (2014) presented a novel finite element (FE) approach for predicting

end cover separation failures in RC beams strengthened in flexure with either externally

bonded or near-surface mounted FRP reinforcement. In the proposed FE approach,

careful consideration is given to the constitutive modelling of concrete and interfaces.

Furthermore, the critical debonding plane at the level of steel tension bars is given special

attention; the radial stresses exerted by the steel tension bars onto the surrounding

concrete are identified to be an important factor for the first time ever and are properly

included in the FE approach. Their proposed FE approach is shown to provide accurate

predictions of test results, including load–deflection curves, failure loads and crack

patterns.

Bencardino and Spadea (2014) carried out numerical analysis with reference to

external strengthened RC beams with a steel reinforced grout system. Through an

appropriate numerical investigation, based on a suitable three-dimensional model,

compared with the results of an experimental investigation, a parametric analysis was also

developed.

Chen et al. (2015) examined the effectiveness of using a dynamic analysis approach in

such FE simulations, in which debonding failure is treated as a dynamic problem and

solved using an appropriate time integration method. Numerical results are presented to

show that an appropriate dynamic approach effectively overcomes the convergence

problem and provides accurate predictions of test results.

Zidani et al. (2015) presented an advanced finite element model using the general

purpose FE software ANSYS to simulate the flexural behaviour of initially damaged

concrete beams repaired with FRP plates. The model is capable to simulate the full history

stages; where the beam is initially loaded to introduce damage, then, after bonding the

FRP plates, the beam is reloaded up to failure. The finite element model has been

43

validated using experimental data in the literature and used to study the effect of concrete-

FRP models, interfacial shear stress distribution, crack pattern, and failure mechanism. In

addition, the effect of plate thickness and the gained load capacity in terms of damage

degree have been also investigated. The predicted results indicated that the load capacity

of all repaired beams is higher than that of the control beam for any damage degree.

Moreover, when repairing highly damaged beams, the most likely expected mode of

failure is plate debonding for any FRP plate thickness

2.4 Optimization in Structural Design

A wide variety of optimization algorithms have been created and studied throughout

the last centuries. The first optimization techniques, like the Gauss steepest descent

developed in the 18th century, were based on pure mathematics. More complex

techniques have been later developed, and the first modern technique, Dantzig's linear

programming, appeared in the 1940's (Dantzig, 1949), to be used by the US military.

Since then, a rising interest in optimization has led to the development of dozens of

different algorithms which can be used in a wide range of applications. Schmit (1960)

recognized the potential for applying optimization techniques in structural design in 1960

(Schmit, 1960). He first used non-linear programming techniques to design elastic

structures.

2.4.1 Gradient-Based Approach

Gradient-based approaches directly use mathematical tools to find optimal solutions.

The gradient-based algorithms are the Sequential Quadratic Programming (SQP)

(Fletcher, 1987) and the Hookes-Jeeves algorithms (Hooke & Jeeves, 1961). The working

principle is that from an initial value, the local gradient information is used to establish a

direction of search at each iteration, until an optimum is reached. These kinds of

algorithms only work with objective functions which are twice differentiable or that can

44

be approximated by terminated first-order or second-order Taylor series expansion

around the initial guessed value. This approach can be used for the optimization heating

systems and has more recently been used for optimization of cooling plants’ control

scheme. While this type of approach has been used in past studies, it suffers from two

major limitations discussed below.

The first limitation of gradient-based methods is that they are prone to local extrema.

Depending on the starting value, they are likely to get trapped in the nearest local optimal

value, missing the actual optimum. Taking several different initial values could

eventually be seen as a solution to overcome this problem, but it would provide little

guarantee, and may become a purely random search. The second major limitation of

gradient-based approaches is that, as stated above, they only work with differentiable or

at least relatively smooth functions. As far as building phenomena are concerned,

functions are very often non-linear problems. Moreover, both discrete and continuous

variables are involved, which may lead to discontinuous outputs.

2.4.2 Gradient-Free Approach

The second and more modern school of optimization techniques, referred to as

‘gradient-free’, relies on stochastic techniques rather than derivatives to determine the

search direction. This allows the exploration of the whole search space, focusing only on

regions of interest. Unlike the techniques previously described, gradient-free approaches

can easily avoid local extrema and have proven their efficiency on optimization problems

where classical methods fail (Goldberg, 1989). Several different algorithms from this

school of optimization have been developed. A review of the predominant ones used for

building applications is detailed by Wetter and Wright (2004). Of all gradient-based

techniques, population-based techniques and more precisely genetic algorithms are

45

predominant, and have proven their efficiencies in hundreds of cases; genetic algorithms

will therefore be discussed in more details.

2.4.3 Genetic Algorithms

A genetic algorithm (GA) is an optimization technique developed by Holland (1975)

in the 1970s and is based on Darwin's theory of evolution. GA's principle is simple,

although unusual. In a nutshell, each solution is referred to as an individual, which may

further produce children, and on which an evolutionary mechanism is applied. GA has

been used in a wide range of studies, from medicine (Lahanas et al., 2003) to

transportation engineering (Syarif & Gen, 2003).

Regarding the efficiency, GA is recognized to enable very detailed optimization and

is capable of finding optimal or near optimal solutions using less computation time than

other algorithms (Kobayashi et al., 1998; Wetter & Wright, 2003). Another advantage of

GA is that it can be used for true multi-objective optimization. GA has been able to

successfully handle multiple objectives, where other evolutionary algorithms such as

particle swarm optimization have failed (Srinivasan & Seow, 2005). One last quality of

GA is that it can perform very well when associated with response surface approximation

methods (Chow et al., 2002).

A main drawback of GA is the high number of calls to evaluation function. In building

applications, these evaluations are generally estimated by an external simulation program

or other simulation software. If accurate results are required, each evaluation can be time

consuming, and thus the complete computational process becomes extremely

unattractive. For instance, for the two-objective optimization of building floor shape,

Wang et al. (2006) used an evaluation tool where each evaluation took 24 seconds (CPU-

time). In that case, the total optimization time, which was mainly due to evaluations, was

68 hours. Based on a simple rule of three, one can expect that, using simulation software

46

where each evaluation would take thirty minutes, a similar optimization would result in a

total optimization time of more than 6 months.

Although the GA method has received much attention in recent years with respect to

discrete optimization, they have a few areas with unanswered questions. For instance,

will they always produce global optima and can they be implemented and tuned to solve

discrete structural optimization problems? Using a practical structural system and a GA

based method efficiently solved a discrete variable problem with constraints. Rajeev and

Krishnamoorthy (1992) efficiently solved a discrete variable problem with constraints.

They showed that even though the GA is not well suited for constrained problems a

penalty-based transformation can be implemented. They also showed that the GA method

is suitable for a parallel computing environment. Near optimal solutions in reasonable

computing times were obtained on large design space layout and sizing problems of steel

roof trusses using a GA by Koumousis and Georgiou (1994). They reported that no clear

rules exist for tuning of the GA parameters and the estimate of the parameters is delicate.

Using the uniform building code as constraints. Camp et al. (1998) developed a GA based

method for optimizing two-dimensional steel frame structures. The method was tested on

30 designs. The method always produced structures satisfying the code standards while

minimizing the weight but the solution was not guaranteed to be global. Lu and Kota

(2005) successfully applied a GA method to a mixed discrete topology and continuous

sizing problem.

Despite the foregoing success, evolutionary algorithm (EAs) by themselves are

unconstrained optimization methods and suffer from lack of generality when applied to

specific engineering problems. That is, the particular encoding from one problem to

another is necessarily different, the formulation of problem constraints and objective

function is specific and the EA control parameters often must be tuned to the specific

47

problem group and sometimes even to the specific problem instance. Alternative methods

of representing problem requirements more generally deserves further investigation.

A common conclusion in the literature with respect to GA is that it requires

considerable user insight and adjustment to the parameters to get reasonable results

(Thanedar & Vanderplaats, 1995).

2.4.4 Optimization of RC Structures

The optimal design for beams was first proposed by Galilei (1950), even though his

calculation was wrong. Haug and Kirmser (1967) were the first to try to use a digital

computer as a tool for the optimal design of this structure element. They reduced the non-

linear optimal design problem to Langrange problem in the calculus of variations. Their

model includes restrictions and tries to minimize the weight of the beam in several

different situations. Venkayya (1971) developed a method to design a structure subjected

to static loading based on an energy criteria and a search procedure. He argued that his

method can efficiently handle a design with multiple load conditions and stress

constraints on size elements. His method has been successfully applied to the design of

trusses, frames and beams. Balaguru (1980) designed an algorithm to calculate the

optimum dimensions and the amount of reinforcements for a doubly reinforced

rectangular beam. Osyczka (1984) applied multi-objective optimization techniques to a

beam design problem. Prakash et al. (1988) proposed a model for the optimal deign of

RC sections in which the cost of steel, concrete and shuttering were included.

Chakrabarty’s model has some similarities to Prokash’s model (Chakrabarty, 1992a;

Chakrabarty, 1992b).

Many researchers have applied different optimization techniques to the design of RC

structures. The crushing strength of concrete was considered as a design variable in

addition to cross-sectional dimensions and steel ratios, for the cost optimization of simply

48

supported and multi-span beams with rectangular and T-shaped cross-sections

(Kanagasundaram & Karihaloo, 1991a, 1991b). They used sequential linear programming

and sequential convex programming techniques, formulating the cost optimization as a

non-linear programming problem. Adamu et al. (1994) developed a method based on

continuum-type optimality criteria, while Han et al. (1996) used discretized continuum-

type optimality criteria. Lepš and Šejnoha (2003) used GAs to optimize RC beams while

Camp et al. (2003) used GAs to optimize structures.

Leroy (1974) derived an equation to find the optimum ratio of steel to concrete area

for a singly reinforced beam based on moment constraints alone. Chou (1977) uses the

Lagrange multiplier method to find the minimum cost design of a singly reinforced T-

beam using the ACI code. Kirsch (1983) presented a simplified three level iterative

procedure for cost optimization of multi-span continuous RC beams with rectangular

cross-sections. He optimized the amount of reinforcement at the first level, the concrete

dimensions at the second level, and the design moments at the third level. Lakshmanan

and Parameswaran (1985) derived a formula for the direct determination of span to

effective depth ratios which can avoid the trial and error approach necessary for the

flexural design of RC sections as per the Indian standard. Coello et al. (1997) presented

a cost optimum design of singly reinforced rectangular beams using GA. They considered

the sectional dimensions and the area of tensile reinforcement as variables in their

optimum design model. Koumousis and Arsenis (1998) presented the application of GAs

for the optimum detailed design of RC members on the basis of multi-criterion objectives

that represent a compromise between a minimum weight design, maximum uniformity

and the minimum number of bars for a group of members.

Some studies on structural optimization deal with minimization of the weight of

structures (Haug & Kirmser, 1967; Karihaloo, 1979; Lakshmanan & Parameswaran,

49

1985; Venkayya, 1971). However, most researchers have worked on the cost optimization

of structures (Al-Salloum & Husainsiddiqi, 1994; Ceranic & Fryer, 2000; Chakrabarty,

1992a; Chakrabarty, 1992b; Friel, 1974a; Kanagasundaram & Karihaloo, 1991a, 1991b;

Perumalsamy & Balaguru, 1980; Prakash et al., 1988). Although the weight of a structure

may be proportional to its cost, minimization of cost should be the actual objective in

economically designing RC structural elements.

Most researchers have used the ultimate load method for the design of beams (

Chakrabarty, 1992a; Chakrabarty, 1992b; Friel, 1974a; Karihaloo, 1979; Perumalsamy &

Balaguru, 1980), whereas a few have used the limit state method (Adamu et al., 1994;

Ceranic & Fryer, 2000; Prakash et al., 1988). While the ultimate load method provides a

realistic assessment of safety, it does not guarantee satisfactory serviceability at service

loads. On the other hand, the limit state method aims for a comprehensive and rational

solution to the design problem by considering safety at ultimate loads and serviceability

at working loads and hence is a better design method.

Kwak and Kim (2008) recently developed a simplified and effective algorithm for the

practical application of optimum design techniques on RC members. Instead of utilizing

a more sophisticated optimization model that requires many design variables and

complicated descriptive functions, the proposed algorithm used a more effective direct

search method to find the optimum member sections from a predetermined section

database. After constructing a database of predetermined RC sections, which were

arranged in the order of increasing resisting capacities, the relationship between the

section identification numbers and the resisting capacities of the sections was established

by regression and was used to obtain an initial solution (section) that satisfies the imposed

design constraints. Assuming that an optimum section exists near the section initially

selected by the regression formula, a direct search is conducted to determine the discrete

50

optimum solution. The optimization of the entire structure is accomplished through the

optimization of individual members.

During the past two decades, considerable progress has been made in the area of

optimizing the design of RC structures using various methods. Most researchers have

worked on the cost optimization of structures, although a few studies deal with the

optimization of weight. Moreover, most of the studies only consider steel as an internal

reinforcement embedded in the concrete. Limited or no studies have been found on the

optimization of FRP strengthened RC beams. Compared to steel, FRP reinforcement

generally possesses a lower modulus of elasticity, which leads to higher reinforcement

strains, wider cracks and larger deflections. Thus, the behaviour of FRP strengthened RC

structures will require the use of the serviceability limit state design method.

2.4.5 Optimization of FRP Strengthened RC Beams

No significant works could be found on the optimization of structural strengthening

systems except a study by Perera and Varona (2009). They used GAs for the discrete

optimization of the design of FRP strengthened RC structures subjected to the limitations

and recommendations specified by the European design guidelines (FIB, 2001). A

description is given of the GA approach that they take to optimize the FRP external

reinforcement used for the flexural and shear strengthening of RC beams. The starting

point for natural selection is a database of FRP laminates and sheets of different sizes and

dimensions, which contains the usual specifications supplied by manufacturers. FRP

laminates were used for flexural strengthening while FRP sheets were applied for shear

strengthening. Each candidate in the database was assigned an identification number, so

that discrete optimization could be performed using GAs. Flexural plate length as well as

the number of sheets were dealt with through discrete values. The objective function was

the cost of strengthening. This can be estimated as the cost of the CFRP plates or sheets

51

plus the cost of the adhesive. The former depends on the volume of composite used for

flexural and shear reinforcement while the latter depends on the surface or the interface

to which the adhesive must be applied. Penalty functions were also included for the

restrictions found in the design guidelines.

2.5 Identification of Research Gaps and Significance of this Study

Externally bonded reinforcement is a commonly practiced method to strengthen

structures. Many studies have been conducted to investigate the effect of different

parameters on the external bonding technique, using steel plates or FRP composites. As

extensive research on this strengthening method has already taken place, a number of

design guidelines on this method have been published in different countries. On the other

hand, NSM reinforcement is a relatively new, though promising technique in the field of

structural strengthening. A number of experimental research works have been conducted

on the NSM strengthening method. Moreover, the ACI has already updated their design

guidelines to include the NSM technique. However, no significant works could be found

on the HSM, which combines the above two techniques. The HSM may eliminate some

of the limitations of the existing two strengthening methods, thus experimental

investigation needs to be conducted on this method.

A number of codes or design guidelines have been published in different countries for

the design of RC structures strengthened with steel and FRP. However, the conventional

practice in the design of RC beams and their structural strengthening systems involves

performing preliminary elastic analyses based on an assumed cross-section and then

checking the member for its adequacy against strength, serviceability and other

requirements as imposed by the design codes. If the requirements are not satisfied, then

the sectional dimensions are modified repeatedly until it satisfies the requirements of the

code. This repetitive process is carried out without considering the relative costs of the

52

component materials of the structure. Therefore, to optimize the total cost of the structure,

a guideline is required to determine the minimum amount of materials needed to design

a functional structure.

The main contributions of the current study are thus: the investigation of the

effectiveness and feasibility of using the HSM for the flexural strengthening of RC

members under monotonic and cyclic loading, the characterization of the experimental

behaviour of RC beams strengthened with NSM steel bars, the presentation of a more

economical strengthening solution, and the development of an optimum design method

for structural strengthening systems. The research is comprised of experimental,

numerical and analytical programs to achieve the stated objectives of the current study.

2.6 Research Questions

Based on the research gaps mentioned in the previous section of this chapter, it is

urgently important to achieve the answers or the solutions to the following research

questions:

i. Is the newly proposed HSM feasible or not?

ii. In comparison to the existing two methods, does the HSM perform better

or not?

iii. Which parameters mostly affect the efficiency of the HSM?

iv. Does strengthening with NSM steel bars and cement mortar give a more

economical strengthening solution without compromising technical

performance?

v. Does the use of optimization approaches make the strengthening design

process more efficient?

53

METHODOLOGY

3.1 Introduction

The research methodology applied in this study has been divided into three parts,

namely experimental investigation, numerical modelling and mathematical optimization.

However, they all share the same goal. The goal of the current research work is to make

a more efficient structural strengthening system. Exploring the use of steel bars and

cement mortar in NSM reduces the cost and hybridizing the existing two methods

improves the technical performance. Therefore, the efficiency of the structural

strengthening system will be increased. The optimization method will also reduce the cost

and increase the efficiency of the system. Section 3.2 describes the experimental setup

including the materials used, the design, preparation and strengthening of the specimens,

instrumentation of the specimens and the test procedure to examine effectiveness of the

use of steel bars and cement mortar in NSM and the proposed HSM. The development of

a semi-numerical model is discussed in Section 3.3. Section 3.4 demonstrates finite

element modelling and Section 3.5 describes the application of mathematical

optimization techniques.

3.2 Experimental Programme

An experimental programme was developed to verify the proposed HSM and the

effectiveness of the use of steel bars with cement mortar in NSM. Experimental data on

loading, deflection, strain and failure mode were obtained. The experimental program

consisted of thirty-three RC beams. The beams were tested under various strengthening

configurations. However, the properties of the basic concrete beam before strengthening

were the same for most specimens, except for a few beams which were given a higher

internal reinforcement ratio. In this section, a general description is provided of the RC

beams and their different fabrication stages, the procedures used to strengthen the beam

specimens, the instrumentation of the beams and the test-setup.

54

3.2.1 Materials Used and Their Properties

3.2.1.1 Concrete and Cement Mortar

Ordinary portland cement (OPC) was used in casting the beams. Crushed stone

(granite) was used as a coarse aggregate and the maximum aggregate size was 20 mm. It

was sieved through a 4.5 mm sieve and air-dried in the concrete laboratory. Natural river

sand was used as a fine aggregate. A sieve analysis was done in accordance with BS 882

to determine the grading of the fine aggregate. The grading of the sand used as fine

aggregate was two. Before casting, the coarse aggregate were washed with water and air

dried in the concrete laboratory to get the saturated surface dry (SSD) condition. Fresh

tap water was used to hydrate the concrete mix during the casting and curing of the beams,

cubes, prisms and cylinders. The concrete mix was designed for 30 MPa strength using

the DOE method. The mix proportions adopted are shown in Table 3.1. The compressive

strengths of the concrete were obtained from three cubes after twenty-eight days curing

according to the British Standard (BS 1881). The average compressive strength was 30

MPa. Cement mortar was also used for NSM strengthened beam. 50% cement and 50%

sand by weight basis were mixed with water to make mortar. The water to cement ratio

of this mortar was 0.50.

Table 3.1: Concrete mix design

Slump

(mm)

Water

Cement

ratio

Concrete (Kg/m3)

Water Cement Coarse

Aggregate

Fine

Aggregate

60-180 0.65 208 320 740 1120

55

3.2.1.2 Internal Steel Reinforcement

Four types of steel bars were used in the preparation of the beam specimens. These

were 12 mm, 10 mm, 8 mm and 6 mm diameter bars. The 12 mm bars were used as

flexural reinforcement. The 12 mm bars were bent ninety degrees at both ends to fulfill

the anchorage criteria. The 10 mm bars were used as hanger bars in the shear span zone.

The 6 mm bars were used for stirrups. 6 mm, 8 mm and 10 mm bars were used for NSM

strengthening purpose. The test data obtained for 6 mm plain bars are shown in Appendix

A.

3.2.1.3 Steel Plate

Mild steel plates were used for strengthening RC beam. The yield and ultimate tensile

strength of the steel plates were 420 MPa and 475 MPa. The modulus of elasticity was

200 GPa. Three different thicknesses of steel plates were used such as 1.5 mm, 2 mm and

2.76 mm. In addition to strengthening, 2 mm thick and 100 mm wide L-shape steel plates

were used for end anchorage.

3.2.1.4 CFRP Plate and Fabrics

The tensile strength and modulus of elasticity of CFRP plates were 2800 MPa and 165

GPa, respectively. The design and ultimate strain of CFRP plates were 0.0085 and 0.017,

according to the manufacturer’s (SIKA) specifications. Fiber in matrix is shown in Figure

3.1. The Sikadur 30 resin has 1% elongation at failure, which is less than the ultimate

elongation of the CFRP plate material (1.9%).

56

Figure 3.1: Fiber in matrix (Badawi, 2007)

Beside the CFRP plate, CFRP fabric was used for both flexural strengthening and end

anchorage. The thickness of this fabric was 0.17 mm. The tensile strength and elastic

modulus of dry fiber was 4900 MPa and 230 GPa, respectively. The elongation at

breaking point was 2.1%.

3.2.1.5 Adhesive

Sikadur 30 epoxy adhesive was used as a bonding agent between the strengthening

materials and the tension surface of the concrete beams. Sikadur 30 is a high strength and

high modulus structural epoxy adhesive. It also has a high creep resistance under long

term loads. According to the manufacturer, its tensile strength at seven days is 24.8 MPa;

it has 1% elongation at failure, and a modulus of elasticity of 11.2 GPa. The bond strength

of Sikadur 30 can vary based on the curing conditions and the bonded materials. Sikadur

30 epoxy adhesive has two components, namely component A and component B.

Component A is white in color and consists of the epoxy resin. Component B is black in

Matrix

Fiber

57

color and consists of the hardener. Component A and component B are mixed together in

3:1 ratio by weight until a uniform grey- colored paste is achieved. No solvent is added.

The paste is then applied to the required surfaces. The surfaces must be prepared before

application. Sikadur 30 reaches its design strength seven days after application.

3.2.2 Design and Preparation of Beam Specimen

All the beam specimens were 2300 mm long, 125 mm wide, and 250 mm deep as

shown in Figure 3.2. The beams were reinforced with two 12 mm diameter steel bars in

the tension zone as the main reinforcement. Two 10 mm steel bars were used as hanger

bars in the shear span and were placed at the top of each beam. For shear reinforcement,

6 mm bars were used and were placed symmetrically apart. The spacing of the shear

reinforcement was 75 mm. Enough shear reinforcements were provided in an amount

calculated to ensure that the beams would fail in flexural. However, certain beams were

given additional reinforcement by using 6 mm stirrups spaced at 40 mm instead. The

various steel bars were arranged to make a reinforcing steel cage before the concrete

casting of each beam. The details of the internal reinforcement used in a typical beam are

shown in Figure 3.2. A typical concrete cover of 30 mm was used.

Figure 3.2: Details of the beam specimens

58

To measure the strain in the tension reinforcement during loading, two 5 mm strain

gauges were mounted at the mid-span of the beams on each rebar. In order to place the

strain gauges, the surfaces of the reinforcing bars were ground to remove the ribs and to

flatten the surfaces. After grinding, the surfaces were cleaned by acetone to remove small

dust particles. To allow the adhesive to set, the strain gauges were left for several hours.

The strain gauges were then connected to wires by soldering. The connection between the

wires and the strain gauges was checked using a multi-meter. After wiring the strain

gauges, they were coated with silicon to protect them from damage during and after the

concrete casting. The reinforcing steel cages were then placed into steel molds. Proper

care was taken to avoid disturbing the strain gauges while the beam was being cast.

The concrete was prepared by mixing cement, sand, coarse aggregate and water in the

concrete mix proportions mentioned above (Table 3.1) using a laboratory drum mixer of

500 kg capacity. Steel molds were used for casting. Before pouring the concrete, the steel

molds were cleaned and greased. After the concrete was placed in the mold, it was

compacted using a poker vibrator. The beams were cast in three layers and each layer was

compacted using a poker vibrator to ensure adequate compaction. During the vibration

process, each penetration was made at a reasonable distance from each other to avoid

bleeding and segregation of the concrete. The subsequent curing was done by covering

the beams with wet hessian cloths for at least two weeks.

Besides the beam, nine 100 mm × 100 mm × 100 mm cubes, three cylinders of 150

mm diameter × 300 mm height and three 100 mm × 100 mm × 500 mm prisms were cast

from the same batch of fresh concrete. These were cured and tested in accordance with

BS standards to determine the compressive strength and flexural strength (modulus of

rapture) of the concrete as shown in Figure A1 in Appendix A.

59

3.2.3 Strengthening of RC Beams

All specimens except control beams were strengthened using various methods.

Specifically, two strengthening methods were used. These were the NSM and HSM.

Strengthening requires careful observation and preparation of the beam. After the beam

specimens were cured for 28 days, they were ready for structural strengthening. Basically,

two types of material were used for structural strengthening, steel and CFRP, but in

various configurations. The basic procedures carried out in strengthening the RC beam

specimens are described in the following subsections.

3.2.3.1 Surface Preparation

The surfaces of both concrete and steel plates require special preparation for proper

bonding between the concrete and strengthening material is used. All dust, laitance,

grease, curing compounds, foreign particles, disintegrated materials and other bond

inhibiting materials must be removed from the bonding surfaces. The concrete surface

has to be clean and sound. In addition, the texture of the coarse aggregate in the concrete

must be exposed. To achieve this, the bonding faces of all concrete beams were ground

with the help of a diamond cutter to obtain a rough surface and to expose the texture of

the coarse aggregate, as shown in Figure 3.3

Figure 3.3: Prepared surface of a concrete beam

60

The grounded concrete surfaces were then cleaned to remove dust, loose particles and

any other foreign material. A wire brush and a high pressure air jet were used to clean the

surface as shown in Figure 3.4. After this surface treatment, putty was applied to fill up

any cavities or holes in the bonding surface of the concrete beam.

Figure 3.4: Compressed air jetting

Figure 3.5: Sand blasted steel plate

61

The surfaces of the steel plates and the CFRP laminates were also prepared. The

bonding surfaces of the steel plates were sand blasted in accordance with Swedish

standards to ensure adequate bonding between the concrete and steel plates. The sand

blasted surfaces of two steel plates are shown in Figure 3.5. The sand blasted steel plates

were then cleaned with acetone to remove small foreign particles and dust. The CFRP

laminates were cleaned using Colma cleaner to remove carbon dust from the bonding

surfaces.

Figure 3.6: Groove cutting

For the beams strengthened using NSM or the HSM, either one or two grooves were

cut along the length of the tension faces of the concrete beams for the placement of the

NSM bars. The grooves were made by making parallel cuts with a diamond concrete saw

as deep as the desired depth (two times bar dia) of the NSM groove. Figure 3.6 shows a

groove being cut into a beam. The grooves were then cleaned using a wire brush and a

high pressure air jet to remove dust and loose particles as shown in Figure 3.4.

62

3.2.3.2 Placement of Strengthening Materials

Strengthening was done using two methods, namely the NSM method and the HSM.

Steel plates, steel bars and CFRP plates were used in various configurations for

strengthening. For the NSM method steel bars were used. For the HSM a combination of

either steel plate and steel bars or CFRP plate and steel bars was used. To bond the

strengthening materials to the surfaces of the concrete beams an epoxy adhesive was used,

namely Sikadur 30. This epoxy was chosen for its excellent engineering properties, which

include its high strength, high modulus, and high creep resistance under long term loads.

To prepare the epoxy adhesive, Sikadur 30, its two components (resin and hardener)

were mixed in a ratio of 3:1 until a uniform grey-colored paste was achieved. In the case

of NSM strengthening, the prepared groove was half-filled with the prepared epoxy

adhesive and then the NSM steel bar was pressed into the centre of groove until the

adhesive flowed around the sides of the bar. Then, the remaining space in the groove was

filled with the epoxy adhesive and levelled using a spatula. The specimens were allowed

to cure for at least seven days before testing. In HSM, the beam specimens were first

strengthened using the NSM method and then using the externally bonded method. In all

cases, the prepared beam specimens were not disturbed for at least seven days to allow

proper curing to take place.

3.2.4 Instrumentation

3.2.4.1 Demec Points

Demec points were installed on the side surfaces of each concrete beam to measure

strain and to determine the position of the neutral axis of the beam sections. The distance

between two horizontally placed Demec points was 200 mm. The concrete surface where

each Demec point was to be installed was grounded to ensure proper bonding. The surface

was then cleaned with acetone to remove dust. After preparing the concrete surface, the

63

Demec points were installed using an adhesive as shown in Figure 3.7 and allowed to set

for at least 24 hours.

Figure 3.7: Demec points on a concrete beam with a strain gauge

3.2.4.2 Electrical Resistance Strain Gauges

Electrical resistance strain gauges were used to measure strain in the steel bars, steel

plates, CFRP plates and concrete. Before casting, the main rebars of each beam were

ground using a mechanical grinder at mid span as shown in Figure 3.8. After grinding,

the surface was cleaned with acetone to remove steel fragments and dust particles.

Figure 3.8: Surface preparation of steel bars to place strain gauges

64

Two 5 mm gauges were attached to the middle of the rebars of each beam by fast

setting adhesive on the top or bottom face of the two main steel rebars as shown in Figure

3.9. These two gauges were used to record the tension strain in the steel rebars. To allow

the adhesive to set properly, the attached strain gauges were left for several hours. The

strain gauges were then connected with wire by soldering as shown in Figure 3.9. The

electrical connection was checked using a multi-meter. The reading was found to be 120

Ω, which is acceptable.

Figure 3.9: Attachment of strain gauges

Silicon was applied on the strain gauges as well as on the necked wire (shown in Figure

3.10) to seal them from water exposure during and after casting. Proper care was taken to

not disturb the electrical resistance strain gauges more than necessary while each beam

was being cast. The connection of the strain gauges was checked again after casting.

65

Figure 3.10: Strain gauges covered with silicone gel

Two 30 mm strain gauges were placed at the middle of the top face of each concrete

beam and at the bottom of the strengthening steel or CFRP plate to measure the concrete

compressive and plate tensile strains. A 30 mm strain gauge was also installed in the

middle of the two lowest Demec points in order to verify demec readings as shown in

Figure 3.7.

3.2.4.3 Linear Variable Displacement Transducers (LVDTs)

One LVDT was used for each beam at the middle of the span for all cases except one

where three LVDTs were used. The LVDT had workable transverse ranges of 50 mm and

were used to measure the deflection of each beam at mid span. All the transducers were

connected to a portable data logger to record the deflections of the beams during testing.

3.2.4.4 Data Logger

The data logger used in this study is a TDS-530. It was used in the testing of each beam

specimen to record the data of several strain gauges placed at different positions, three

LVDTs and loads from an Instron testing machine. The strain gauges were connected as

1G3W120Ώ to the data logger and the unit of strain measurement was micro-strain. The

66

LVDTs were connected as 4GAGE to the data logger and the unit of deflection

measurement was millimeters.

3.2.4.5 Digital Extensometer

The bending deformation of each beam under loading was measured from its Demec

points using a digital extensometer. This was used to estimate the strain profile of each

beam and to determine the position of the neutral axis. The attachment of Demec points

on the side surface of beam specimens is described in section 3.2.4.1.

3.2.4.6 Dino-lite Digital Microscope

This instrument (Figure 3.11) was used to measure the crack widths in concrete beam

specimens during tests. Using this device, crack widths could be measured with an

accuracy of up to 0.001 mm. The adjustable lens allowed very sharp pictures of the cracks

to be taken, from which the crack widths could be estimated accurately. However, the

spacing between different cracks along the length of the beams had to be measured

manually.

Figure 3.11: Dino-lite digital microscope for crack width measurement

67

3.2.5 Test Setup and Procedure

All beam specimens were tested in four-point bending as shown in Figure 3.12. All

specimens were simply supported using steel roller support (Static) and elastomeric

bearing pads (fatigue) and were subjected to two point loading. The distance between the

two supports was 2000 mm and the distance between the two loading points of the

spreader beam was 700 mm. The resulting shear span to depth ratio was about 3. For the

static load tests, the actuator was loaded and moved down at a rate of 1 mm/min so that

readings from the data logger could be taken and visible cracks measured easily.

Figure 3.12: Experimental set up

Each beam was lifted and positioned on to the supports leaving 150 mm lengths of

beam at both ends so that the beams were simply supported by a span of 2000 mm. The

LVDTs were then placed appropriately, ensuring that the transducers touched the plate or

Strain gauge

LVDT

Support

Spreader beam

Load cell

68

concrete. All the strain gauges and LVDTs were connected to the data logger and the data

logger was calibrated. After recording all data from the data logger, the spreader beam

was placed on top of the beam specimens to ensure two-point loading. The data from the

data logger were again recorded.

The tests were conducted using a closed-loop hydraulic Instron Universal Testing

Machine. For repeated loading, a closed-loop system programmed to deliver a sinusoidal

load at a frequency of 3 Hz was used. The load span, load set point, frequency and preset

number of cycles were controlled by an electronic controller. The sinusoidal waveform

was checked through computer.

3.2.6 Test Matrix

The beam specimens were divided into five groups. The first group, series C (Figure

3.13), is the control group, where the beams were left unstrengthened. The second group,

series P (Figure 3.14), was strengthened with externally bonded steel or CFRP plates. The

data for this series was entirely taken from a previous study by another researcher, Alam

(2010) in same laboratory. This was done to compare the effectiveness of the HSM with

the external EBR. In the third group, series N (Figure 3.15), the beams were strengthened

with NSM steel bars. In the fourth group, series H (Figure 3.16), the beams were

strengthened using the HSM where either a combination of steel plates and steel bars or

CFRP plates and steel bars were used. The fifth group, series SH (Figure 3.17), was where

HSM was applied on the sides of the beams. Within each group, various configurations

and dimensions of the different strengthening materials were used.

Table 3.2 gives a detailed overview of the beam specimens tested and analysed in this

research. Table 3.2 gives the beams that were directly tested by this researcher. Notation

used in Table 3.2 has been described in Table 3.4 and Table 3.5. Table 3.3 shows the

69

details of beams that were tested in a previous study (Alam, 2010), and is included in this

research.

Table 3.2: Test matrix1

No. Series Notation Description Descriptions of

Strengthening

1 C Series

(Figure 3.13)

CB Control beam -

2

N Series

(Figure

3.15)

N2S6C Beam strengthened with

NSM steel bar and cement

mortar

2 ϕ 6 mm bar

3 N2S6E Beam strengthened with

NSM steel bar and epoxy

2 ϕ 6 mm bar

4 N2S6EC Beam strengthened with

NSM steel bar, cement

mortar and epoxy

2 ϕ 6 mm bar

5 N1S8E Beam strengthened with

NSM steel bar and epoxy

1 ϕ 8mm bar

6 N1S8C Cracked beam strengthened

with NSM steel bar and

cement mortar

1 ϕ 8mm bar

7 N3S8C Beam strengthened with

NSM steel bar and cement

mortar

3 ϕ 8mm bar

8 N1SH8C Beam (higher internal ratio)

strengthened with NSM steel

bar and cement mortar

1 ϕ 8 mm bar

9 N2SS8C Beam strengthened with

NSM steel bar (side of beam)

2 ϕ 8 mm bar

10

H Series

(Figure

3.16)

H1B8S19L73W2T

Beam strengthened with

hybrid bonded steel plate

and steel bar

1ϕ 8 mm

Steel plate

(2×73×1900 mm3)

11 H1B8S16L73W2T

Beam strengthened with

hybrid bonded steel plate

and steel bar

1 ϕ 8 mm

Steel plate

(2×73×1650 mm3)

12 H1B6S16L73W2T

Beam strengthened with

hybrid bonded steel plate

and steel bar

1ϕ 6 mm

Steel plate

(2×73×1650 mm3)

13 H2B8S19L73W2T

Beam strengthened with

hybrid bonded steel plate

and steel bar

2 ϕ 8mm

Steel plate

(2×73×1900 mm3)

14 H2B6S19L73W2T

Beam strengthened with

hybrid bonded steel plate

and steel bar

2 ϕ 6 mm

Steel plate

(2×73×1900 mm3)

15 H2B6S19L73W2.76T

Beam strengthened with

hybrid bonded steel plate

and steel bar

2 ϕ 6 mm

Steel plate

(2.76×73×1900 mm3)

16 H2B6S19L125W2T

Beam strengthened with

hybrid bonded steel plate

and steel bar

2 ϕ 6mm

Steel plate

(2×125×1900 mm3)

17 H1B8SD19L73W2T

Beam (different spacing of

shear reinforcement)

strengthened with hybrid

steel plate and steel bar

1 ϕ 8 mm

1-Steel plate

(2×73×1900 mm3)

18 H2B6S19L125W1.5T

Beam strengthened with

hybrid bonded steel plate

and steel bar

1 ϕ 10 mm

Steel plate

(1.5×73×1900 mm3 )

70

Table 3.2 continue 19

H Series

(Figure

3.16)

H1B8S19L73W2TAS

Beam strengthened with

hybrid bonded steel plate

and steel bar and shear

strengthening with CFRP

fabric

1ϕ 8 mm

Steel plate

(2×73×1900 mm3)

CFRP fabric –

Width = 200 mm

20 H1B8S19L73W2TAF

Beam strengthened with

hybrid bonded steel plate

and steel bar and shear

strengthening with CFRP

fabric

1ϕ 8mm

Steel plate –

(2×73×1900 mm3)

CFRP fabric

(Width = 100 mm)

21 H1B8F19L80W1.2T

Beam strengthened with

hybrid bonded CFRP plate

and steel bar

1ϕ 8 mm

CFRP plate

(1.2×80×1900 mm3)

22 H1B8F16L80W1.2T

Beam strengthened with

hybrid bonded CFRP plate

and steel bar

1ϕ 8 mm

CFRP plate

(1.2×100×1650 mm3)

23 H1BP8F16L80W1.2T

Beam strengthened with

hybrid bonded CFRP plate

and steel bar

1ϕ 8 mm

1CFRP plate

(1.2×100×1650 mm3)

24 H1BP6F16L80W1.2T

Beam strengthened with

hybrid bonded CFRP plate

and steel bar

1ϕ 8 mm

1-CFRP plate

1.2x100x1650 mm3

25 H2BP6F16L80W1.2T

Beam strengthened with

hybrid bonded CFRP plate

and steel bar

1 ϕ 8 mm

CFRP plate

(1.2×100×1900 mm3)

26 H1B8F19L80W1.2TA

F

Beam strengthened with

hybrid bonded CFRP plate

and steel bar

2 ϕ 6mm

CFRP plate

(1.2×100×1900 mm3)

27 H1B6FR19L100W.17

T

Beam strengthened with

hybrid bonded CFRP fabrics

and steel bar

1ϕ 6mm

1-CFRP fabric

(.165×100×1900 mm3)

28 SH Series

(Figure

3.17)

SH2S61900L100W2T

Beam strengthened with

side-applied hybrid bonded

CFRP plate and steel bar

2 ϕ 6mm

2-Steel plate

(2×50×1900 mm3 )

29

Fatigue

Series

CBF50 Control for fatigue -

30 CBF80 Control for fatigue -

31 PSF Beam strengthened with

externally bonded steel plate

1-Steel plate

(2.76×100×1900 mm3)

32 NSF Beam strengthened with

NSM steel bar

1ϕ 8 mm

33 HSF Beam strengthened with

hybrid bonded steel plate

and steel bar

1ϕ 8mm

Steel plate

(2×100×1900 mm3)

71

Table 3.3: Test matrix2 (Taken from Alam (2010)) Sl. no Series Notation Description Description of

strengthening

1 C Series

(Figure 3.13)

CB1 Control beam

2

P series

(Figure 3.14)

PS19L73W2.76T Beam strengthened with

Steel plate (Alam, 2010)

1-Steel plate

(2×73×1900 mm3)

3 PS16L73W2.76T Beam strengthened with

Steel plate (Alam, 2010)

1-Steel plate (2×73×1650

mm3 )

4 PF19L80W1.2T Beam strengthened with

CFRP plate (Alam, 2010)

1- CFRP plate

(1.2×80×1900 mm3)

5 PF16L80W1.2T Beam strengthened with

CFRP plate (Alam, 2010)

1-CFRP plate

(1.2×80×1650 mm3)

Figure 3.13: Series CB beam (Control beam)

Figure 3.14: Series P (EBR)

Figure 3.15: Series N (NSM strengthening)

Figure 3.16: Series H (HSM strengthening)

1650-1900 mm

1650-1900mm

mm

1650-1900 mm

72

Figure 3.17: Cross-section of series SH beam (HSM at sides)

Table 3.4: Description of beam notation for HSM.

H 1 B 8 S 19L 73W 2T AF

H 1 B 8 S 19L 73W 2T AF

Name

of

series

No.

of

bar

Position

of Bar

Diameter

of bar in

NSM

Materials for

strengthening

Length

of plate

Width

of plate

Thickness

of plate

Anchorage

H =

HSM

N =

NSM

P =

EBR

SH =

Side

HSM

B =

bottom 6 = 6 mm S=Steel

19L=

1900

mm

73W =

73 mm

2T =

2 mm

AF =

Anchorage

with Full

wrap

S = side 8 = 8 mm F=FRP

16L=

1650

mm

80W =

80 mm

2.76T =

2.76 mm

AS =

Anchorage

with side

wrap

SD=Steel but

different

spacing of

internal shear

reinforcement

125W=

125 mm

1.5T =

1.5 mm

Table 3.5: Description of beam notation for NSM strengthening.

N 3 S 8 C

N 3 S 8 C Name of series No. of bar Material for strengthening

with position

Diamerter of bar Adhesive type

N-NSM 3=3 Nos S = Steel bar with bottom E = Epoxy

SS = Steel bar with side

face

8=8 mm C = Cement

mortar

SH = Steel bar with higher

internal reinforcement

EC = 50% Epoxy

and 50% Cement

along the length

73

3.3 Development of Semi-numerical Model

Numerical analysis is the study of algorithms that use numerical approximation (as

opposed to general symbolic manipulations) for the problems of mathematical analysis.

The main objective of numerical analysis is to obtain approximate solutions while

maintaining reasonable bounds on errors. Iterative methods are more common in

numerical analysis. Starting from an initial guess, iterative methods form successive

approximations that converge to the exact solution. The number of steps needed to obtain

the exact solution is large that an approximation is accepted. The method of mathematical

optimization (alternatively, optimization or mathematical programming) can be used to

reduce these large number of steps. Therefore, application of mathematical optimization

in numerical analysis is referred to semi-numerical method.

Mathematical optimization is the selection of a best constituent from some set of

available alternatives based on certain criteria. An optimization problem comprises of

maximizing or minimizing a function by scientifically choosing the values of input

variables from an allowable set and estimating the value of the function. The

generalization of optimization theory and techniques to other formulations comprises a

large area of applied mathematics. More generally, optimization includes finding "best

available" values of some objective function given a defined set of constraints.

Application of mathematical optimization technique make the semi-numerical method

more efficient because of less number of steps or iterations. However, it has still some

drawbacks. In current study, tension stiffening effect of internal reinforcement was not

considered. Incorporation of proper tension stiffening effect will make the semi-

numerical model more perfect and robust.

74

3.3.1 Material Properties

3.3.1.1 Concrete

Developing a model for the behaviour of concrete is a complex task. Concrete is a

semi-brittle material and behaves differently in tension and in compression. The ultimate

uniaxial tensile strength and compressive strength are required to define a failure surface

for the concrete. In tension, the concrete stress–strain curve is linearly elastic up to the

ultimate tensile strength. After this value, the concrete cracks and the strength reduces to

zero. The tensile strength of concrete is usually 8 - 15% of its compressive strength (Shah

et al., 1995). Figure 3.18 shows a typical stress-strain curve for normal weight concrete

(Bangash, 1989).

Figure 3.18 : Stress-strain relationship of concrete (Bangash, 1989)

The stress in the concrete and corresponding strain can be expressed by the Equations

(3.1) (3.2) and (3.3) according to Hognestad’s parabola:

σc = fc′ [2

εc

εc′

− (εc

εc′)

2

] (3.1)

Concrete Softening

Stress

Str

ain

75

εc′ = 2

fc′

Ec (3.2)

Ec = 5700(fc′)1/2 (3.3)

where:

σc = the concrete stress corresponding to a given concrete strain (εc),

fc = the concrete compressive strength,

εc = the concrete stain corresponding to a given concrete stress (σc),

εc = the concrete strain corresponding to the concrete compressive strength, and

Ec = Young’s modulus of concrete.

3.3.1.2 Steel Bars and Plates

The compression and tension reinforcement are assumed to be elastic-plastic with a

1% strain hardening slope (bi-linear behaviour). The idealized stress-strain relationship

is shown in Figure 3.19.

Figure 3.19: Stress-strain relationship of steel bar and plate

Equations (3.4) and (3.5) express the relationship between steel stress and the

corresponding strain.

76

σs = εsEs if εs < εy (3.4)

σs = εsEs + Esp(εs − εy) If εs > εy (3.5)

where:

σs = the steel stress corresponding to a given steel strain (s εs),

fy = the steel yield stress corresponding to the steel yield strain (y εy),

εs = the steel strain corresponding to a given steel stress,

εy = the steel yield strain corresponding to the steel yield stress,

Es = the modulus of steel before yielding,

ESP = the modulus of steel after yielding.

3.3.1.3 CFRP Composite

The stress-strain curve for a CFRP plate is linearly elastic up to failure. The

relationship is given in Equation (3.6).

σcfrp = Ecfrp εcfrp (3.6)

where:

σcfrp = the CFRP stress corresponding to a given CFRP strain, and

Ecfrp = Young’s modulus of CFRP.

3.3.2 Modeling Methodology

In this study, section analysis is used to estimate the strains and the curvatures along

the length of the beam for modeling by using the Equations (3.7) to (3.18). It is a familiar

topic to engineers as the idea is strongly embedded in codes of practice. Sectional analysis

lies between graphical hand method of analysis and finite element computer program

(Bentz, 2000). In using the sectional analysis approach, the problem of determining the

response of a reinforced concrete structure to applied loads is broken up into two

interrelated tasks. First, the sectional forces at various locations in the structure caused by

77

the applied loads are determined. This step is usually performed assuming that the

structure remains linearly elastic. Then the response of a local section to the sectional

forces is determined. The second step, which is the sectional analysis, the non-linear

characteristics of cracked reinforced concrete are taken into account. Figure 3.20 shows

the strain, stress, and force distribution on a section of a beam.

Figure 3.20: Strain, stress and force distribution on a section

εs = εc

d − c

c (3.7)

εp = εc

h − c

c (3.8)

Fcc = bcfc′ (

εc

εc′) (1 −

εc

3εc′) (3.9)

Fs = AsEsεs if εs < εy (3.10)

Strain Stress Acting Force

Cross-section

78

Fs = As(fy + 0.01Esp(εs − εy)) if εs > εy (3.11)

Fnsm = AnsmEnsmεnsm if εnsm < εy (3.12)

Fnsm = Ansm(fy + 0.01Esp(εnsm − εy)) if εsnsm > εy (3.13)

Fp = ApEpεp if εs < εy (3.14)

dx = [1 −

23

−εc

εc′

1 −εc

3εc′

] (3.15)

Fc − Fs − Fnsm − Fp − Fct = 0 (3.16)

Fc(h − dx) − Fs(h − d) − Fnsm

dc

2− Fct {(h − c) −

2dcr

3} = Mint (3.17)

Mext = Mint (3.18)

3.3.3 Deflection Prediction Model

3.3.3.1 Steps to Predict the Deflection:

The calculation procedure to predict the load-deflection of beam specimen (control

and strengthened) beam is as follows:

i. Assume a given external applied load on the beam.

ii. Calculate the external moment.

iii. Assume a strain at the compression fiber of the concrete.

iv. Assume the neutral axis depth.

v. Calculate the strains in the tension steel, NSM steel and steel/CFRP

reinforcement by using triangular rule.

vi. Calculate stresses and forces in the compression concrete, tension steel,

NSM steel bar and steel/CFRP plate.

79

vii. Evaluate force equilibrium equations. If not in equilibrium, change the

neutral axis depth in step 4 and repeat steps 4 to 7 until in equilibrium.

viii. If the forces are equilibrium, calculate internal moment by taking moment

against strengthening plate level.

ix. Compare the calculated internal moment to the external moment obtained

in step 2. If not equal, change the assume strain in step iii and repeat steps

iii to ix.

x. If external moment is equal to internal moment, calculate the deflection

using semi-numerical approach described in sub-section 3.3.3.2 and record

the load and deflection data.

xi. Calculate the deflection and record the load and deflection data.

xii. Apply the load increment and repeat steps 2 to 10 until failure.

3.3.3.2 Semi-numerical Approach

The sectional analysis is usually done by making assumption of two unknown, strain

of any material and depth of neutral axis, and applying trial and error approach. These

two unknown could be solved by using two equilibrium equations (force and moment

equilibrium). However, the direction of assumption can be complicated due to divergence

problem. This problem can be eliminated by the application of mathematical

programming (non-linear programming and genetic algorithm) technique. Therefore,

complicated several steps will be reduced to one easy step. The calculation procedure to

predict the load-deflection curve of beam specimen (control and strengthened) beam is as

follows:

i. Assume a given external applied load on the beam.

ii. Calculate the external moment.

80

iii. Apply an optimization algorithm to estimate concrete strain and the neutral

axis depth by using an objective function as equation (3.19) and constraint

as εc < 0.0035 at the compression fiber of concrete and εp <0.0065 rupture

of FRP fiber.

iv. Calculate curvature an element of the beam and curvature distribution along

the beam according to the procedure described in Badawi (2007).

v. Calculate the deflection by integrating the curvature.

Objective function can be expressed using Equation (3.19) given below:

Minimize error = (Mext − Mint) 2 + (Fcom − Ften)2 (3.19)

3.3.4 Flexural Strength Model

The main objective of flexural strength model is to estimate ultimate flexural capacity

of the beam. Since Mext is equal to Mint according to moment equilibrium theory,

maximum value of Mext calculated from Equation (3.17) will be ultimate flexural capacity

of the beam when either εc, compression fiber of concrete will reach 0.0035 or εp, strain

of FRP fiber will reach 0.0065.

3.3.5 Debonding Strength Model

3.3.5.1 Modelling Methodology

The objective of this subsection is to develop a simple and rational methodology for

predicting the debonding failure load for strengthened concrete beams that can be used in

practical design applications. The methodology is employed in two steps: 1) predicting

the principle stresses at the plate end; and 2) comparing these stresses with the limiting

stresses in an appropriate concrete failure criteria.

81

Jones et al. (1988) recommended the use of elastic shear stress (τ) calculated from

classical beam theory to predict the interfacial shear stress at plate ends. It is a simple

procedure with a strong theoretical background. To calculate the interfacial shear stress

the following expression is used. The elastic shear stress expression is:

τ =V0Afbfnfyf

Icbf (3.20)

where:

Vo = shear force at the plate curtailment location,

Af = area of the plate,

nf = modular ratio of the late (Ef /Ec),

yf = distance of the plate from the neutral axis,

Ic = transformed moment of inertia of beam cross section in terms of the concrete and

bf = width of the plate.

El-Mihilmy and Tedesco (2001) modified and simplified Robert’s expressions to

account for the non-linearities that exist at the concrete-adhesive interface and developed

expressions for calculating the interfacial normal stress directly from interfacial shear

stress (Equation (3.21) and Equation (3.22)).

σx = 1.3(αf)1

2 𝜏 (3.21)

αf = √Gatf

taEf (3.22)

Elastic normal stress that is perpendicular to the beam’s cross section is mainly

responsible for flexural cracking. This normal stress is also responsible for increasing the

principle stress that causes diagonal cracks at plate ends. Concrete cover separation is

believed to be accelerated by such diagonal cracks. This elastic normal stress can be

82

estimated using classical bending theory from the external moment at the plate ends

(Equation (3.23)).

σx = M

I(df − c) (3.23)

Finally the principle stresses, σ1 and σ2, can be calculated using th Mohr theory of

stress transformation from elastic normal stress, σx, interfacial normal stress σy and

interfacial shear stress τxy. The major principle stress, σ1 is responsible for causing

diagonal crack while the minor principle stress, σ2 reduces the uniaxial tensile strength of

concrete through biaxial action of these stress. The position of elastic normal stress, σx,

interfacial normal stress σy and interfacial shear stress τxy are shown in Figure 3.21. The

expression for the principle stresses are given in Equation (3.24)

Figure 3.21: The principle and interfacial stress

σ1, σ2 = (σx+σy

2) ∓ √(

σx − σy

2)

2

+ 𝜏𝑥𝑦2 (3.24)

3.3.5.2 Failure Criteria for Debonding Failure

The concrete at the strengthening plate in a strengthened beam is under a state of

combined shear, τ and biaxial tensile stresses σx, and σy which result from the combination

83

of beam flexural and plate-peeling stresses (Figure 3.22). Thus, the two-dimensional

principle stress state in the concrete is usually either tension-tension or tension-

compression, depending on the magnitude of the shear stress. Figure 3.22 shows the

typical biaxial failure criteria for concrete.

Figure 3.22: Typical biaxial failure criteria for concrete (Tysmans et al., 2015)

ftu = ft +−σ2

fc′

(3.25)

When the principle stress, σ1 becomes greater than the bi-axially applied reduced

tensile strength of concrete (ftu), the diagonal cracks occur at the plate end. This diagonal

cracking subsequently initiates and further accelerates the concrete separation process.

The above debonding prediction model directly considers elastic shear and normal stress.

It is therefore completely based on theoretical concept. It can consider and distinguish

both end delamination and concrete cover separation.

84

3.4 Finite Element Modelling

3.4.1 Introduction

The finite element method is a useful technique in solving highly non-linear problems

in continuum mechanics as reinforced concrete structures exhibit highly non-linear

behaviour, especially approaching failure load. Numerical models have been developed

using the ABAQUS program to predict the load deflection behaviour of reinforced

concrete beams strengthened by FRP applied at the bottom of the beams. For many

structural material, such as steel and aluminium which have well-defined constitutive

properties, this finite element method works very well. However, when the constitutive

behaviour is not so straight forward, like concrete in which discrete cracking occurs, the

task is more difficult. The objective of this part of the study is to establish a reliable,

convenient and accurate methodology for analysing FRP strengthened RC beams which

can correctly represent global beam behaviour.

One of the advantages of finite-element models is to capture quantities that are

virtually impossible to measure experimentally. In addition, they provide insight effects

of micro- and macro-cracking on the interfacial behaviour and they allow us to obtain

better results which may vary significantly from researcher to researcher, such as FRP

strain.

As a part of the present study, experiments were performed on strengthened RC beams

to investigate the flexural behaviour and to determine the ultimate failure load. The beam

is subjected to two-point quasi-static load up to failure. The material properties and their

constitutive modelling, analysis approach, verification of the finite element model, and

special modelling considerations and modifications are outlined in this section. A series

of RC beams strengthened with steel and FRP plates at the bottom were tested to failure

under a four-point bending load. By comparing numerical results with experimental ones,

85

the proposed finite element model has been validated and can be used for further

prediction of this type of failure.

3.4.2 Material Properties and their Constitutive Model

The materials used in the model engage steel reinforcing bars, concrete, steel and FRP

plates. Reliable constitutive models related to steel reinforcing bars, steel plates, and

concrete are obtainable in the ABAQUS material library. Thus, their input properties and

related constitutive models are briefly discussed.

3.4.2.1 Concrete

Development of a constitutive model to simulate the behaviour of concrete is a

challenging task. Concrete is a semi-brittle material and exhibit different performance in

compression and tension. Concrete was modelled using a solid element with eight nodes

and with three translation degrees of freedom at each node. The concrete solid element in

the ABAQUS model is called ‘C3D8R’. The concrete has an uni-axial compressive

strength (fc′) selected as 30 MPa according to the experimental result. Under uni-axial

compression, the concrete strain (ε0) corresponding to the ultimate compressive stress (fc′)

is usually around the range of 0.002 to 0.003. A representative value recommended by

ACI Committee 318 and used in the analysis is εo = 0.003. The value for Poisson’s ratio,

ν = 0.2 was used for the isotropic inelastic stages. The concrete damaged plasticity model

(CDP) was used for defining concrete material behaviour in the inelastic range. The main

failure mechanisms of concrete in CDP include: (1) tensile cracking, and (2) compressive

crushing of the concrete.

The compressive stress-strain behaviour of concrete is simulated using a uniaxial non-

linear constitutive model. The program computes the concrete compressive stress-strain

curve based on the input of stress versus inelastic strain. The concrete behaviour under

axial tension is assumed to be linear until the formation of the initial cracking at the peak

86

stress known as failure stress. Post failure stress is defined in the program in terms of

stress versus cracking strain. This behaviour allows for the effect of the interaction

between the concrete and the reinforcement rebar through introducing tension stiffening

to the softening side of the curve.

3.4.2.2 Reinforcement

A classical metal plasticity model is applied for the non-linear material effects of steel

reinforcement cast in concrete. Incremental theory is used in the plasticity model to relate

load, deformation and stress non-linearity, once yielding has occurred. For an arbitrary

load history, the final state of stress and deformation can be determined by accounting for

the history of stress and strain. The history is taken into account by formations that relate

increments of stress to increments of strain.

An elastic-perfectly plastic material was used for steel with an equal behaviour in

tension and compression. The steel reinforcement used in the beam is assumed to have

the yielding stress of 500 MPa while its modulus of elasticity is assumed to be Es 200

GPa. The stress–strain curve of the reinforcing bar is assumed to be elastic-perfectly

plastic as shown in Figure 3.19. The steel reinforcement has a Poisson’s ratio of 0.3.

Perfect bonding between the steel and the concrete is presumed. The embedded element

option was used for connecting the reinforcement element to the concrete element, and

steel reinforcement was used as the embedded element while concrete was used as the

host element.

3.4.2.3 Carbon Fiber Reinforced Polymer

The CFRP is designated as a linear elastic orthotropic material, because the composite

is unidirectional and the behaviour is essentially orthotropic. The uniaxial behaviour of

the FRP composites used in this study is assumed to be linear-elastic until failure with no

87

post-peak or ductile behaviour. Failure of these materials is occurred when the strain, εpu

reaches to its rupture stress, fpu as shown in Figure 3.23. Since the FRP is used primarily

to carry tensile forces, it has stiffness in only one direction (along the fibres), thus no

lateral and shear resistance is observed. Because the fiber reinforced plastics are relatively

thin compared to the concrete beam, they are modeled by the 4-node shell elements (six

degrees of freedom per node).The FRP shell elements are attached to the bottom surface

of the concrete beam directly.

The modulus in the fibre direction is a significant factor, because the composite is

mainly stressed in the fibre direction. The experimental value of 165 GPa is assigned for

the elastic modulus in the fibre direction where the unidirectional CFRP material is used

in the experimental study. This modulus of elasticity was specified by the model. For

CFRP-concrete interface, full bond assumption was made for the interaction between FRP

and concrete surfaces.

Figure 3.23: Stress-strain diagram of CFRP

3.4.3 Boundary Conditions

The boundary conditions were set in the model to mimic the experimental test

conditions. One end of the beam was restrained in three degrees of freedom in the Ux,

Uy, and Uz, directions, representing hinge support. In this scenario, the support was

88

allowed to rotate in every direction. The other end of the beam in the model was assumed

as a roller support that is restrained in Uy.

3.4.4 Loads on RC Beams

In order to incorporate gravity and lateral loads in the finite element (FE) model, two

steps were defined in the FE simulation. The gravity load was simulated in the first step

as uniform pressure applied at the top of the beam. Load step sizes were automated by

ABAQUS.

3.4.5 Discretization

The structural member is broken down into finite elements to model the composite

beam. Since more than one type of material and interface is considered in the analysis,

different types of elements are required to discretize the structure. The structural member

is modelled as a mesh of finite elements. A wide range of elements are available in

ABAQUS. Among these, continuum elements are the most comprehensive as they can be

used in almost any linear/non-linear stress-displacement and crack propagation analysis.

Both two- and three-dimensional (2D and 3D) continuum elements are available however,

2D continuum elements can adequately investigate the behaviour of the beams in this

research. The 2D elements can be either triangular (3 or 6 nodes) or quadrilateral (4 or 8

nodes).

The concrete is modelled using continuum elements. Continuum elements are

provided with first-order (linear) and second-order (quadratic) interpolation and careful

consideration must be used as to which is more appropriate for the application. First-order

elements use linear interpolation to obtain displacements at nodes, whereas second-order

elements use quadratic interpolation to obtain displacements at nodes. ABAQUS offers

two integration options.

89

Linear reduced-integration continuum elements are employed throughout the analysis

with a fine mesh for their ability to withstand severe distortion in plasticity and crack

propagation applications. All the elements in the model were purposely assigned the same

mesh size to ensure that two different materials each share the same node. The type of

mesh selected in the model was structured. The mesh element for the concrete, rebar and

FRP laminate element were 3D solid, 2D truss and shell, respectively.

3.4.6 Finite Element Procedure

Displacement-controlled finite element methods are commonly applied in structural

analysis and result in a system of equations corresponding unknown nodal deformation

to specified loads by the stiffness matrix. Based on the calculated displacements, stresses

and strains are computed. The equations engaged are derived from suitable structural

theory and satisfy the following equilibrium (relate stresses to applied forces),

compatibility (strains to displacement), and constitutive (stresses to strains). Together,

these relationships are used to form the displacement based FEA equations in the matrix

form. Cracking has been modelled using predefined crack line in ABAQUS.

The matrix equation is then solved for the displacement vector. Solving the equations

allows us to go directly from forces to displacements. Strains and stresses are then

computed from the displacement results. Shape functions are used to describe

displacements. They are created through the use of Lagrangian interpolation to perform

the necessary function of relating local coordinate position to global coordinate position.

Once the displacements are calculated, they can be related to the strains within the

element. The determination of strain requires partial differentiation of the displacement

function with respect to the global coordinates.

90

3.5 Mathematical Optimization

“Optimal” means the most economical solution (Kasperkiewicz, 1995). Optimization

is the act of estimating the best results under certain circumstances. In the design,

construction and maintenance of any system, several decisions take place. The ultimate

objective of these decisions is to either minimize cost or to maximize the required benefit.

To optimally solve engineering problems, it is essential to convert design problems into

optimization formulations, including objective functions and constraint functions.

Optimization procedures try to seek the ‘best’ solutions for a desired objective function,

f(x), while satisfying the prevailing constraints. Maximization can be easily converted

into a minimization problem since the maximization of f(x) is equivalent to the

minimization of – f(x) (Perera & Varona, 2009).

3.5.1 Algorithm for Optimum Design Solution

Optimization of RC beams and their strengthening systems involves choosing design

parameters in such a way that cost is minimized, while behavioural and geometrical

constraints as recommended by design codes are also satisfied (Saini et al., 2007). In

operational research, methods to find optimum solutions, such as mathematical

programming techniques, are often studied. Mathematical programming methods are

helpful in finding the minimum function of a number of variables under a certain set of

constraints. The optimization tasks often uses mathematical maximization or

minimization of an objective function f(xi) of n design variables, xi, subjected to m

equality constraints, gj, and n inequality constants, hk. In more realistic terms,

optimization refers to finding the best possible arrangement for a given problem.

Presented below is a formulation of the needed objective function.

In this study, the objective function is the total cost of the strengthening system

subjected to applied force. The behavioural constraints are the requirements for flexural

91

strength and serviceability, while the geometrical constraints can be the upper limits on

beam arising from practical considerations. It is now essential to search for a

configuration characterized by a minimum price, which yet complies with all selected

allowable strength and serviceability limits.

3.5.2 Objective Function

The problem of optimization largely depends on the type and nature of the objective

function. The selection of the objective function thus has a significant influence on the

optimization problem. This function is utilized to demonstrate a measure of how the

different variables have performed in the problem domain. In the case of a minimization

problem, the best solution will have the smallest possible numerical value of the related

objective function (Perera & Varona, 2009).

Objective functions also form hyper-surfaces. When the objective function surfaces

are illustrated along with the constraint surfaces on the design space, the optimum

location can be easily predicted graphically as shown below in Figure 3.24.

92

Figure 3.24: Function plot depicting optimum for a two design variable set

(Menon, 2005)

The optimization of FRP strengthened RC beams can be formulated by using total

material cost as an objective function. The cost of FRP strengthening systems depends

not only on the volume or weight of FRP material used, but also on the amount of adhesive

used. Hence, the design variables are the dimensions of FRP materials and the quantity

of adhesive. These variables can be changed to minimize the cost of the strengthening

system.

The mathematical form of the cost function i.e. the objective function C (Equation

3.25) for the design of FRP strengthened RC beam is as follows:

C = CfbftfLf + CabfLf (3.26)

where:

C = the cost of the FRP strengthening system,

Cf = the unit price of the FRP plate,

93

Ca = the unit price of the epoxy adhesive,

bf = the width of the FRP plate,

tf = the thickness of the FRP plate, and

Lf = the length of the FRP plate.

For this study, it can reasonably be assumed that the unit cost of the CFRP plate is RM

1.70 per cubic centimetre and the unit price of epoxy adhesive is RM 1.00 per cubic

centimetre.

3.5.3 Design Constraints

In structural optimization problems, technical performance and practical limitations

are satisfied through the application of constraint functions. Constraints reduce the extent

of the design space to be searched in accordance with the objectives that have to be

achieved. Constraints include flexural constraints and serviceability constraints.

3.5.3.1 Flexural Constraints

The design guidelines proposed by the concrete society, TR55, on the flexural

strengthening of RC beams with FRP are formulated in the optimization problem through

constraint functions, gi. Flexural resistance of the FRP strengthened RC beam must be

greater than the external moments caused by the applied loads. These constraints provide

acceptable levels of safety against ultimate limit states. The design loading and the design

strength of the materials are required to evaluate these limit states. This constraint is

presented in the following form (Equation 3.26).

M ≤ Mr (3.27)

where:

M = the design ultimate moment of the strengthened section, and

Mr = the resisting bending moment of the strengthened section.

94

The resisting bending moment of FRP strengthened RC beams can be estimated by

using load factors and safety factors as required by the TR 55 guidelines, based on strain

compatibility, internal force equilibrium and by taking into account the failure mode of

the strengthened beam. The resisting bending moment of the strengthened section of a

singly reinforced beam can be calculated by the Equation (3.28) which is given below.

The balanced resisting moment of the strengthened beam, Mr,b, can be calculated by using

Equation (3.29) and Figure 3.25, if the design ultimate moment exceeds the balanced

resisting moment.

Mr = Fsz + Ff(z + (h − d)) (3.28)

Mr,b = (0.67 fcu

γmc) b × 0.9(z + (h − d)) (3.29)

Figure 3.25: Stress and strain distribution of balanced failure

where:

x = h (εfu/εcu+1) = depth of neutral axis,

h = over all depth,

εfu = design ultimate failure strain of FRP = εfk/γmF,

εfk = ultimate failure strain of FRP,

γmF = factor of safety against ultimate failure strain of FRP,

95

εcu = ultimate strain of concrete=0.0035,

d = effective depth,

z = lever arm,

Fs = force on steel reinforcement = (fy/γms) As,

fy = yield strength of steel,

γms = factor of safety against steel yield strength,

As = area of steel, Force acting on FRP,Ff = ffAf,

Af = tfbf, stress in FRP, ff = Efd(εcft-εcit), design modulus of FRP,

Efd = Efk/γmE,

Efk = modulus of elasticity of FRP,

γmE = factor of safety against modulus of FRP,

εcft = final strain of FRP = εcu(h-x)/x, and

εci t = initial strain before strengthening.

The design ultimate moment of a simply supported beam with uniformly distributed

load and a clear span l is calculated as follows:

𝑀 =𝑤𝑙2

8 (3.30)

3.5.3.2 The Constraints against Separation Failure

The RC beam strengthened externally with FRP can fail prematurely due to separation

of the FRP plate. There are two different types of failure mechanisms: peeling and

debonding. This is still a controversial subject among the researchers and a lot of research

is going on to develop a precise method to avoid premature plate separation.

Separation due to peeling usually occurs at the ends of the FRP plate due to the abrupt

termination of the plate. The shear stresses and normal stresses are concentrated in the

adhesive layer due to the deformation of FRP plate under applied loads. A number of

factors affect the magnitude of these shear and normal stresses. Generally, end peeling

96

can be prevented by limiting the magnitude of the longitudinal shear stress and extending

the FRP plate beyond the theoretical cut-off point. According to field experience in FRP

installation, the longitudinal shear stress should be limited to 0.8 N/mm2. The longitudinal

shear stress, τ, can be calculated using the Equation (3.31):

𝜏 =𝑉𝛼𝑓𝐴𝑓(ℎ − 𝑥)

𝐼𝑐𝑠𝑏𝑎 (3.31)

where:

V = ultimate shear force,

αf = Efd/Ec, short term modular ratio,

Efd = modulus elasticity of FRP,

Ec = modulus elasticity of concrete,

ba = width of adhesive layer which is normally equal to width of beam, bw, and

Ics = second moments of area of strengthened concrete equivalent crack section.

Regarding the extension of FRP plates, Neubauer and Rostasy (1997) proposed a

simple model that is accepted in the TR55 guideline. The maximum ultimate bond force,

Tk and the corresponding maximum anchorage length, lt,max that are needed to activate

this bond force can be calculated using the Equation (3.32), Equation (3.33) , Equation

(3.34):

τk, max = 0.5 kbbf √Efdtffctm (3.32)

ly,max = 0.7√Efdtf

fctm

(3.33)

97

kb = 1.06 √(2 −

bf

bw

1 +bf

400

) ≥ 1 (3.34)

where:

bw = beam width, and

fctm = 0.18(fcu)2

3 (3.35)

It is also recommended that, where the FRP is terminated in the span, a minimum

anchorage length of 500 mm should be provided. Debonding failure which normally

occurs away from the plate end can be prevented by limiting the strain in the FRP to 0.8%

for uniformly distributed loading and to 0.6% when there is a combination of high shear

forces and bending moment.

3.5.3.3 Serviceability Constraints

Serviceability constraints are formulated in terms of limits on the steel reinforcement

and concrete stress. TR 55 requires that the stresses in the steel reinforcement and

concrete at working loads should not exceed 0.8fy and 0.6fcu, respectively in order to avoid

excessive deformation of the structure. The material stress can be calculated using the

elastic principle. The equivalent transformed section for long term loading has to be

determined by making an assumption that modular rations of steel to concrete, αe and

FRP to concrete, αf can be calculated using the following formula.

αe = Es

0.5 Ec

(3.36)

αf = Efd

0.5 Ec (3.37)

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3.5.4 Application of Optimization Method

3.5.4.1 Non-linear Programming

Non-linear problems can be solved using several methods. A model in which the

objective function and all of the constraints (other than integer constraints) are smooth

non-linear functions of the decision variables is called a non-linear programming (NLP)

or non-linear optimization problem. Such problems are intrinsically more difficult to

solve than linear programming (LP) problems. They may be convex or non-convex, and

an NLP solver must compute or approximate derivatives of the problem functions many

times during the course of the optimization process. Since a non-convex NLP may have

multiple feasible regions and multiple locally optimal points within such regions, there is

no simple or fast way to determine with certainty that the problem is infeasible, that the

objective function is unbounded, or that an optimal solution is the “global optimum”

across all feasible regions.

The Non-linear Solving method uses the Generalized Reduced Gradient (GRG)

method as implemented in Lasdon and Waren’s GRG2 code. The GRG method can be

viewed as a non-linear extension of the Simplex method, which selects a basis, determines

a search direction, and performs a line search on each major iteration – solving systems

of non-linear equations at each step to maintain feasibility. The reduced gradient method

also known as the ‘Frank and Wolfe’ algorithm, is an iterative method for non-linear

programming. Other methods for non-linear optimization include Sequential Quadratic

Programming (SQP) and Interior Point or Barrier methods.

3.5.4.2 Genetic Algorithm

A simple genetic algorithm was applied to solve the problem of the optimization of

FRP strengthened RC beams using a continuous search space. Genetic algorithms cannot

handle constraints explicitly. Therefore, it is essential to transform all constraints into

99

penalty functions. In using genetic algorithms, a number of genetic operations like

generation, selection, crossover and mutation are performed.

Generation is an operation that creates a population of candidate solutions as a starting

point which is usually random. The population size used in this study was 100. Among

the three selection operators, tournament was applied in this application. Crossover and

mutation make the genetic algorithm more powerful. Crossover forms a new chromosome

from two parental chromosomes by a reproduction operation. In this case, single point

crossover was used. Mutation creates diversity among the population by changing a gene.

The mutation rate used in this study was 0.05. The optimization problem of this study

was solved by applying a simple genetic algorithm using the previously mentioned

parameters.

100

RESULTS AND DISCUSSION

4.1 Introduction

This chapter presents the results of this study and discusses the results. Section 4.2

presents the results and discussion of experimental investigation. The results include

strength, deformation, damage and failure characteristic of the specimens. Another

purpose of experimental investigation on the NSM technique is to compare it with HSM.

Some parametric studies were done but they were not carried out primarily for

investigating the effect of different parameters, rather they tried to identify the most

suitable configuration to achieve the best performance. A brief fatigue behaviour is also

discussed in this section. Verification of semi-numerical and finite element modelling is

discussed in Sections 4.3 and 4.4, respectively. Section 4.5 provides example solutions of

the mathematical optimization technique in a structural strengthening system.

4.2 Result of Experimental Investigation

The extensive data obtained from the experimental investigation are presented in this

section. Sub-section 4.2.1 presents the test data of the properties of the materials used for

the preparation of beam specimens. The achievement of experimental research objectives

is discussed in sub-section 4.2.2 to sub-section 4.2.6.

4.2.1 Material Properties

The average concrete cube strength of all tested beams was 29.35 MPa and the

modulus of rupture shown was found to be 3.85 MPa. Test results showed some slight

variations in the concrete strengths and modulus of rupture although they were cast from

the same mix design. The average concrete cube strengths and modulus of rupture of each

tested beam was given in Appendix A. The measured yield and ultimate tensile strengths

of the 6, 8, 10, 12 mm steel bars were shown in Table 4.1. The modulus of elasticity for

all the steel bars was 200 GPa. The test data obtained for 6 mm plain bars are shown in

101

Appendix A. The yield and ultimate tensile strength of the steel plates are 420 MPa and

475 MPa. The modulus of elasticity is 200 GPa.

Table 4.1: The properties of steel bar

Bar diameter

(mm)

Yield strength

(MPa)

Ultimate strength

(MPa)

Modulus of Elasticity

(GPa)

6 580 650

200

8 551 641

10 520 572

12 551 641

4.2.2 Experimental Behaviour of Steel HSM Strengthened Beams

4.2.2.1 Load Carrying Capacity and Failure Mode

A summary of the flexural behaviour of all tested beams strengthened using HSM with

steel bars and steel plates is shown in Table 4.2. The summary is given in terms of first

crack load, yield load, flexural loading capacity and failure mode. As shown in Table 4.2,

the addition of steel bars and steel plates increased the ultimate load capacity by 32% to

72% as compared to the control beam. On the other hand, in the previous study, the

ultimate load of an EBR strengthened beam increased by 37% as compared to the control

beam (Sena-Cruz et al., 2012). In this study, yield load of the beam also increased after

strengthening. The yield load of the beam was sometimes not distinguished because of

early debonding. The first crack load of strengthened beams increased most significantly

as compared to the control beam. These results have proven the effectiveness of HSM to

increase the flexural capacity in accordance with Objective (i).

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Table 4.2: First crack, yield and failure (and modes) load of HSM-steel

Beam no

First

crack

load

(kN)

Increase

in first

crack

load (%)

Bar

yield

load

(kN)

Failure

load

(kN)

Increase

in failure

load (%)

Mode of

failure

CB 12.5 - 72 80.0 - Flexural

failure

H1B8S19L73W2T 40.0 220 120 132.0 65 Cover

separation

H1B8S16L73W2T 58.0 364 100 105.6 32 Cover

separation

H1B6S16L73W2T 60.0 380 90 102.0 27 Cover

separation

H2B8S19L73W2T 48.0 284 100 108.3 35 Cover

separation

H2B6S19L73W2T 30.0 140 90 109.0 37 Cover

separation

H2B6S19L73W2.76T 40.0 220 - 130.0 63 Cover

separation

H2B6S19L125W2T 62.0 396 - 115.0 44 Cover

separation

H1B8SD19L73W2T 40.0 220 - 125.0 56 Cover

separation

H1B8S19L73W2TAS 53.0 324 - 135.0 68

Flexural

failure

(concrete

crushing)

H1B8S19L73W2TAF 40.0 220 - 137.0 71

Flexural

failure

(Concrete

crushing)

H1B8S19L73W1.5T 40.0 220 - 137.3 72 Cover

separation +concrete

crushing

SH2B6S19L100W2T 60.0 380 - 123.0 53

Flexural

failure

(Concrete

crushing)

The failure modes of all beams strengthened with HSM steel plates and bars are shown

in Figure 4.1 to Figure 4.12. The failure modes of most of these beams were found to be

very close to each other i.e. concrete cover separation initiated by a diagonal tension

crack. Concrete cover separation is the most commonly reported mode of failure (Kang

et al., 2012). This type of failure is generally demonstrated by a crack forming in the

103

concrete at or near the plate end, which spreads to the level of the tension reinforcement

and then progresses horizontally, along the level of the reinforcement, resulting in

separation of the concrete cover. The un-strengthened control beam, CB, failed, as

expected, in flexure with extensive yielding of the tension steel, followed by crushing of

the concrete in the compression zone.

Figure 4.1: Debonding failure mode of H1B8S19L73W2T

Figure 4.2: Debonding failure mode of H1B8S16L73W2T

104

Figure 4.3: Debonding failure mode of H1B6S16L73W2T

Figure 4.4: Debonding failure mode of H2B8S19L73W2T

Figure 4.5: Debonding failure mode of H2B6S19L73W2T

105

Figure 4.6: Debonding failure mode of H2B6S19L73W2.76T

Figure 4.7: Debonding failure mode of H2B6S19L125W2T

Figure 4.8: Debonding failure mode of H1B8SD19L73W2T

106

Figure 4.9: Flexure failure mode of H2B6S19L125W1.5T

Figure 4.10: Flexure failure mode of H1B8S19L73W2TAS

Figure 4.11: Flexure failure mode of H1B8S19L73W2TAF

107

Figure 4.12: Flexure failure mode of SH2B6S19L100W2T

4.2.2.2 Effect of Strengthening on Deflection and Cracking Behaviour

The deflection and reduction in deflection due to HSM strengthening at 20 kN, 40 kN,

and 60 kN service loads are shown in Table 4.3. The deflection of the strengthened beams

was reduced compared to the control beam due to increased stiffness.

Table 4.3: Reduction in deflection due to HSM strengthening

Beam No.

Load at 20 kN Load at 40 kN Load at 60 kN

Deflection

in mm

(LVDT)

Reduction

(%) over

CB

Deflection

in mm

(LVDT)

Reduction

(%) over CB

Deflection

in mm

(LVDT)

Reduction

(%) over CB

CB 1.34 - 4.34 - 6.92 -

H1B8S19L73W2T 1.00 25 2.47 43 4.07 41

H1B8S16L73W2T 0.72 46 1.84 58 2.97 57

H1B6S16L73W2T 1.30 3 2.46 42 4.74 32

H2B8S19L73W2T 1.26 6 2.26 48 3.14 55

H2B6S19L73W2T 1.26 6 2.48 43 3.43 50

H2B6S19L73W2.76T 1.18 12 2.12 51 3.00 57

The crack width increased with increased loading according to the data obtained. The

first crack loads of the beams are shown in Table 4.2. The strengthened beams,

H1B8S19L73W2T and H1B8S16L73W2T, had higher cracking load compared to that of

the control beam.

108

4.2.2.3 Comparison of HSM with EBR using Steel Plates and Bars

In this section, the HSM strengthened beams (H1B8S19L73W2T and

H1B8S16L73W2T) are compared to the corresponding EBR beams (PS19L73W2.76T

and PS16L73W2.76T). The detailed experimental behaviour of these two HSM

strengthened beams will be analyzed, interpreted and compared with the corresponding

EBR beam. Other HSM strengthened beams will be used for parametric study.

(a) Effect of HSM strengthening on Ultimate Load

Figure 4.13 shows the effect of hybridization on the ultimate load of the strengthened

RC beams. In both cases (with plate length 1900 mm and 1650 mm), the failure load of

the HSM strengthened beams (H1B8S19L73W2T and H1B8S16L73W2T) was greater

than that of the corresponding EBR beams (PS19L73W2.76T and PS16L73W2.76T). The

amount of strengthening materials used was almost same (total cross-sectional area = 200

mm2) for HSM and corresponding EBR but improvement in HSM was significantly

higher. Specifically, the improvement in the debonding failure loads of

H1B8S19L73W2T and H1B8S16L73W2T was 27% and 24%, respectively as compared

to the improvement of PS19L73W2.76T and PS16L73W2.76T. This improvement was

achieved in two ways: 1) reduction of plate thickness, 2) increased surface area, as

mentioned in the research background of chapter 1. The increase in surface area leads to

improved performance, and this is demonstrated by comparing the failure load of

H2B6S19L73W2.76T (130 kN) and PS19L73W2.76T (104 kN) with same plate

thickness (2.73 mm). Though the plate thickness of H2B6S19L73W2.76T and

PS19L73W2.76T are the same, the failure load of H2B6S19L73W2.76T (HSM) is 26 kN

(25%) higher than that of the PS19L73W2.76T (EBR). Similar improved performance

was found in the externally bonded reinforcement on grooves (EBROG) method, where

only contact surface area increased (Mostofinejad & Shameli, 2013). It has further proved

the effectiveness of HSM and it is more efficient than EBR.

109

Figure 4.13: Comparison of failure load between HSM and EBR

(b) Deflection Characteristics

Deflection data was collected from both the LVDTs and the actuator position of the

Instron Universal Testing machine. The LVDTs were removed immediately after failure

initiation to avoid probable damage. Deflections calculated from the position of the

actuator are also presented in the load deflection diagram in order to observe the actual

deformability of the beams as far as possible. The load versus mid-span deflection curves

of H1B8S19L73W2T, PS19L73W2.76T and the control beam, CB are shown in

Figure 4.14. The deflections of the strengthened beams were lower than that of the

control beam as the stiffness of the strengthened beam increased due to the presence of

the strengthening steel plate and steel bar. However, the deflection of the HSM

strengthened beams, H1B8S19L73W2T and H1B8S16L73W2T, was almost similar to

the EBR beams, PS19L73W2.76T and PS16L73W2.76T, because a similar amount of

steel was used in strengthening. The load versus mid-span deflection curves of

H1B8S16L73W2T, PS16L73W2.76T and the control beam, CB are shown in Figure 4.15.

110

Figure 4.14 : Load-deflection of CB, H1B8S19L73W2T and PS19L73W2.76T.

Figure 4.15: Load-deflection of CB, H1B8S16L73W2T and PS16L73W2.76T

According to the deflection data obtained from actuator positions, the deformability of

the HSM strengthened beams was nearly similar to that of the control beam although the

ultimate load decreased significantly. However, the maximum loads of the HSM

0

20

40

60

80

100

120

140

0 10 20 30 40 50

Lo

ad

(k

N)

Deflection (mm)

CB(actuator)

CB(lvdt)

H1B8S19L73W2T(Actuator)

H1B8S19L73W2T(lvdt)

PS19L73W2.76T(lvdt)

0

20

40

60

80

100

120

0 10 20 30 40 50

Lo

ad

(k

N)

Deflection (mm)

CB(lvdt)

CB(Actuator)

H1B8S16L73W2T(lvdt)

PS16L73W2.76T(lvdt)

111

strengthened beams after debonding were even more than the maximum load of the

control beam. The ductility index at ultimate load of the HSM strengthened beams

(15/12=1.25) was almost similar to that (12/10=1.2) of control beam. This is another

important advantages of HSM technique.

(c) Cracking Behaviour

The cracking behaviour of the HSM strengthened beam improved because of improved

composite action through hybridization. Improvement in the first crack load of the HSM

strengthening technique is shown in Figure 4.16. The first crack loads of

H1B8S19L73W2T and H1B8S16L73W2T increased 14% and 65% over the EBR beams

PS19L73W2.76T and PS16L73W2.76T, respectively.

Figure 4.16: Improvement of first crack loading in HSM strengthening

(d) Internal Reinforcing Bar Strain

The strains in the internal reinforcing steel bars and the reduction in these strains due

to strengthening at 20 kN, 40 kN, and 60 kN service loads are shown in Table 4.4. The

bar strains in strengthened beams were significantly reduced. Consequently, according

Hooke’s law, the stress in the bars should also be reduced and therefore, the fatigue life

112

of the strengthened beams should increase according to the S-N curve relation of steel

bars (Helagson & Hanson, 1974; Moss, 1982). However, differences in bar strain

reduction between the HSM and the EBR were not noticed clearly.

Table 4.4: Bar strain at different service loads

Beam No.

Load at 20 kN Load at 40 kN Load at 60 kN

Bar

Strain

Reduction

(%)

Bar

Strain

Reduction

(%)

Bar

Strain

Reduction

(%)

CB 793 - 1661 - 2507 -

H1B8S19L73W2T 360 55 785 53 1021 59

H1B8S16L73W2T 299 62 583 65 708 72

PS19L73W2.76T 303 62 606 64 910 64

PS16L73W2.76T 485 39 970 42 1456 42

(e) Efficiency of HSM

Figure 4.17 shows the amount of steel required to strengthen concrete beams and the

corresponding increase in load carrying capacity of beams strengthened with EBR and

HSM. As shown in Figure 4.17, although HSM uses a smaller amount of steel, it increases

the load carrying capacity of the beam by 65% as compare to control beam. On the other

hand, the performance of the EBR only increases by 30%.

113

Figure 4.17: Efficiency of the HSM

4.2.2.4 Effect of Plate and Bar Length, Bar Dia. and No. of Grooves

Improvement in the flexural capacity of the strengthened beams depends on various

parameters. Therefore, it is very important to take into account different factors that can

have a major influence on the overall results. In this study, the effect of strengthening

with different configurations was investigated. However, strengthening with different

configurations was investigated mainly to identify optimum arrangements to achieve the

best improvement in flexural performance of RC beams strengthened with steel plates

and bars using the HSM. The effect of individual parameters on the performance was not

a primary concern of this study.

(a) Effect of Plate and Bar Length

The plate and bar length influenced the flexural performance of the strengthened beam.

The plate and bar length are always equal in all HSM strengthened beams. These lengths

have influence flexural performance. The effect of plate and bar length on the

performance of strengthened beams is shown in Figure 4.18. Based on the experimental

372.85 382.812

65

30

0

10

20

30

40

50

60

70

0

50

100

150

200

250

300

350

400

450

HSM EBR

Perfo

rm

an

ce(%

)

Am

ou

nt

of

stee

l (i

n C

ub

ic c

en

tim

eter

)

Strengthening Method

Amount of steel

Performance

114

data of H1B8S19L73W2T, H1B8S16L73W2T, PS19L73W2.76T and PS16L73W2.76T,

it can be said that increasing plate length results in increased failure loads. This is a

common observation in studies on EBR strengthening. Increasing the plate length reduces

the distance between the plate end and the support, which is an influential parameter in

end debonding behaviour of externally bonded plates (Täljsten, 1997).

Figure 4.18: The effect of plate and bar length on failure load

(b) Effect of Bar Diameter

Bar diameter has a significant influence on the flexural resistance of normal RC beams.

However, in NSM or HSM, increasing the strengthening bar diameter reduces the amount

of adhesive and thereby may affect performance of the bond. Hence, it is important to

investigate the influence of bar diameter on the strengthening performance. Figure 4.19

shows the effect of bar diameter on failure load. Data collected from beams

H1B8S16L73W2T, H1B6S16L73W2T, H2B8S19L73W2T and H2B6S19L73W2T were

132

105.6 104

85

1.91.65

1.91.65

0

1

2

3

4

5

6

0

20

40

60

80

100

120

140

H1B8S19L73W2T H1B8S16L73W2T PS19L73W2T PS16L73W2T

Len

gth

(m

)

Load

(kN

)

Failure load (kN) Length (m)

115

used to analyze this parameter. As shown in Figure 4.19, the failure load increased with

increasing bar diameter when one bar was used in the NSM groove of the HSM

strengthened beams (H1B8S16L73W2T and H1B6S16L73W2T). However, when two

bars were used (H2B8S19L73W2T and H2B6S19L73W2T), the failure load decreased

with increasing bar diameter. Thus, the effect of bar diameter on the strengthening

performance of HSM beams is controversial. Although increasing the number of bars

provides additional reinforcement to the concrete beam, it decreases both edge clearance

and clear spacing between two adjacent grooves. This increases the possibility of edge

breakage. The beam specimens used in this study may not have had enough width to place

two bars with sufficient clearance. This may have led to accelerated concrete separation

due to early edge breakage. Similar results were found in Bilotta et al. (2015)’s study

where an increase in the number of grooves caused break down the concrete cover rapidly.

Figure 4.19: The effect of bar diameter

105.6102

108.31 109

8

6

8

6

0

2

4

6

8

10

12

14

16

18

20

0

20

40

60

80

100

120

H1B8S16L73W2T H1B6S16L73W2T H2B8S19L73W2T H2B6S19L73W2T

Bar

dia

(m

m)

Fai

lure

load

(kN

)

116

(c) Effect of Number of Bars or NSM Grooves

Each strengthening bar used requires a separate groove to place the bar in the RC beam.

Thus, the number of bars used in strengthening is equal to the number of grooves. Figure

4.20 shows the effect of the number of grooves or bars on the performance of beams

strengthened using the HSM. The experimental data of H1B8S19L73W2T and

H2B8S19L73W2T were used to investigate this effect. As shown in Figure 4.20, failure

load decreased when the number of bars or grooves increased. This issue has been

discussed in the previous sub-section.

Figure 4.20: The effect of number of bars or grooves

4.2.3 Experimental Behaviour of CFRP-HSM Strengthened Beam

4.2.3.1 Load Carrying Capacity and Failure Mode

Table 4.5 summarizes the flexural behaviour of the tested beams strengthened using

the HSM with CFRP in terms of first crack load, yield load, flexural loading capacity and

failure mode. As shown in Table 4.5, the addition of steel bars and CFRP plates increased

117

the ultimate load capacity by 35% to 104% as compared to the control beam. The yield

load of the beam also increased after strengthening. The first crack load of the

strengthened beams increased significantly compared to the control beam. The addition

of a steel bar and CFRP fabrics in the form of HSM also increased the load capacity by

43%.

Table 4.5: First crack, yield and failure (and modes) load of HSM-CFRP

Beam no

First

crack

load

(kN)

Increase in

first crack

load (%)

Bar

yield

load

Failure

load

Increase

in failure

load (%)

Mode of

failure

CB 12.5 - 72 80 - Flexural

failure

H1B8F19L80W1.2T 30.0 146 120 133.0 66 Cover

separation

H1B8F16L80W1.2T 35.0 187 100 129.8 62 Cover

separation

H1BP8F16L80W1.2T 28.0 129 107 107.0 34 Cover

separation

H1BP6F16L80W1.2T 40.0 233 100 120.0 50 Cover

separation

H2BP6F16L80W1.2T 40.0 233 90 127.0 57 Cover

separation

H1B8F19L80W1.2TAF 32.0 162 - 164.0 104 Flexural

failure

H1B6FR19L100W.17T 27.0 126 - 114.0 43 Flexural

failure

The failure modes of the beams in the above table are shown in Figure 4.21 to Figure

4.27. The failure modes of most of the beams strengthened using the HSM with CFRP

were found to be very close to each other i.e. concrete cover separation initiated by a

diagonal crack. Concrete cover separation is a commonly reported mode of failure. This

type of failure is generally demonstrated by a crack forming in the concrete at or near the

FRP plate end, propagating to the level of tension reinforcement and then progressing

horizontally, along the level of the reinforcement, resulting in a separation of the concrete

cover. Similar to the unstrengthened control beam, CB, which failed in flexure with

extensive yielding of the tension steel, followed by crushing of the concrete in the

118

compression zone, the beams strengthened with CFRP fabrics and steel bars failed in the

desirable flexural failure mode as shown in Figure 4.27.

Figure 4.21: Debonding failure mode of H1B8F19L80W1.2T

Figure 4.22: Debonding failure mode of H1B8F16L80W1.2T

Figure 4.23: Debonding failure mode of H1BP8F16L80W1.2T

119

Figure 4.24: Debonding failure mode of H1BP6F16L80W1.2T

Figure 4.25: Debonding failure mode of H2BP6F16L80W1.2T

Figure 4.26: Flexure failure mode of H1B8F19L80W1.2TAF

120

Figure 4.27: Flexure failure mode of H1B6FR19L100W.17T

4.2.3.2 Effect of Strengthening on Deflection and Cracking Behaviour

The deflection and reduction in deflection due to HSM at 20 kN, 40 kN, and 60 kN

service loadings are shown in Table 4.6. The deflection of the strengthened beams was

reduced compared to the control beam due to increased stiffness of the strengthened

beams.

Table 4.6: Reduction in deflection due to HSM strengthening with FRP

Beam No. Load at 20 kN Load at 40 kN Load at 60 kN

Deflection

(mm)

Reduction

(%)

Deflection

(mm)

Reduction

(%)

Deflection

(mm)

Reduction

(%)

CB 1.34 - 4.34 - 6.92 -

H1B8F19L80W1.2T 1.18 12 2.83 35 4.09 41

H1B8F16L80W1.2T 0.68 49 2.00 54 3.32 52

H1BP8F16L80W1.2T 0.86 36 2.14 51 3.51 49

H1BP6F16L80W1.2T 0.96 6 2.33 48 3.72 55

H2BP6F16L80W1.2T 1.26 6 2.48 43 3.43 50

H1B8F19L80W1.2TAF 0.83 38 2.83 35 4.09 41

H1B6FR19L100W.17T 1.17 14 3.32 23 6.71 3

121

The crack width increased with increased load. The first crack loads of all HSM CFRP

beams are shown in table Table 4.6. The strengthened beams, H1B8F19L80W1.2T and

H1B8F16L80W1.2T, showed higher cracking loads compared to that of the control beam.

4.2.3.3 Comparison of HSM with EBR

In this study, the HSM strengthened beams H1B8F19L80W1.2T and

H1B8F16L80W1.2T, are comparable to the EBR beams, PF19L80W1.2T and

PF19L80W1.2T6L80W1.2T. The detailed experimental behaviour of these two HSM

strengthened beams will be analyzed, interpreted and compared with corresponding EBR

beams. The other HSM strengthened beams will be used to investigate the effect of

strengthening with different configurations.

(a) Effect of HSM Strengthening on Ultimate Load

Figure 4.28 shows the effect of hybridization with CFRP on the static failure

performance of the strengthened RC beams. In both cases (with plate length 1900 mm

and 1650 mm), failure loads of the HSM strengthened beam (H1B8F19L80W1.2T and

H1B8F16L80W1.2T) were greater than that of the corresponding EBR beams

(PF19L80W1.2T and PF19L80W1.2T6L80W1.2T). Specifically, the improvement of

debonding failure loads of H1B8F19L80W1.2T and H1B8F16L80W1.2T are 9% and

36% more than that of PF19L80W1.2T and PF19L80W1.2T6L80W1.2T. This

improvement was achieved by increasing the bonding surface area with the same plate

thickness (1.2 mm).

122

Figure 4.28: Comparison of Ultimate load between HSM and EBR

(b) Deflection Characteristics

The load versus mid-span deflection curves of H1B8F19L80W1.2T, PF19L80W1.2T

and CB are shown in Figure 4.29. The deflections of the strengthened beams were lower

than that of the control beam because the stiffness of the strengthened beam was greater

than that of the control beam due to the presence of the strengthening CFRP plate and

steel bar. However, the deflection of HSM strengthened beams, H1B8F19L80W1.2T and

H1B8F16L80W1.2T, was similar to the EBR beams, PF19L80W1.2T and

PF19L80W1.2T6L80W1.2T, perhaps due to similar amounts of strengthening material

being used. The load versus mid-span deflection curves of H1B8F16L80W1.2T,

PF19L80W1.2T6L80W1.2T and CB are shown in Figure 4.30.

EBR

HSM

123

Figure 4.29: Load-deflection of CB, H1B8F19L80W1.2T and PF19L80W1.2T

Figure 4.30: Load-deflection of CB, H1B8F16L80W1.2T and PF16L80W1.2T

Controversially, the deformability of the HSM strengthened beams were nearly similar

to the deformability of the control beam although ultimate loads increased significantly.

However, as loads after debonding were more than the yield load of the control beam, it

cannot be directly said that the ductility of the HSM strengthened beams was reduced

significantly.

124

(c) Cracking Behaviour

The cracking behaviour of the beams strengthened with CFRP improved because of

improved composite action through hybridization. Improvement in the first crack loads

of the CFRP-HSM strengthened beams is shown in Figure 4.31. The first crack load of

H1B8F19L80W1.2T and H1B8F16L80W1.2T increased 14% and 65% over the cracking

loads of the EBR beams PF19L80W1.2T and PF19L80W1.2T6L80W1.2T, respectively.

Figure 4.31: Improvement in first crack loads of HSM strengthened CFRP

beams

(d) Internal Reinforcing Bar Strain

The strains in the internal reinforcing steel bars and the reduction of these bar strains

due to strengthening were measured at 20 kN, 40 kN, and 60 kN service loads, as shown

in Table 4.7. The internal bar strains in strengthened beams were significantly reduced.

According to Hooke’s law, reduced bar strains result in reduced bar stresses. Thus, the

fatigue life of the strengthened beams should have increased according to the S-N curve

relation of steel bar (Helagson & Hanson, 1974; Moss, 1982). However, any difference

125

in the reduction of bar strains between the CFRP-HSM strengthened beams and the

corresponding EBR beams was not clearly noticeable.

Table 4.7: Bar strain at different service loads

Beam No. Load at 20 kN Load at 40 kN Load at 60 kN

Bar

Strain

Reduction

(%) over

CB

Bar

Strain

Reduction

(%) over

CB

Bar

Strain

Reduction

(%) over CB

CB 793 1661 2507

H1B8F19L80W1.2T 197 75 792 52 1305 48

H1B8F16L80W1.2T 222 72 629 62 1212 52

PF19L80W1.2T 200 75 800 52 1572 37

PF16L80W1.2T 212 73 970 42 1605 36

4.2.3.4 Effect of Plate and Bar Length, Bar Dia. and No. of Grooves

Strengthening with different configurations was investigated to identify the most

suitable arrangement to achieve the best improvement in flexural performance of the RC

beam strengthened with FRP and steel bars.

(a) Effect of Plate and Bar Length

The effect of plate and bar length is shown in Figure 4.32. Based on the experimental

data of H1B8F19L80W1.2T, H1B8F16L80W1.2T, PF19L80W1.2T and

HF16L80W1.2T beams, increasing the plate length resulted in increased failure loads,

which is expected behaviour commonly observed in experiments. Increasing the plate

length reduced the distance between the plate end and the support which is an influential

parameter in end debonding behaviour of externally bonded reinforcement (Täljsten,

1997).

126

Figure 4.32: The effect of plate and bar length on failure load

(b) Effect of Bar Diameter

Bar diameter has a significant influence on the flexural resistance of normal RC beams.

However, in NSM and HSM, increasing the bar diameter reduces the amount of adhesive

and thereby may affect the performance of the bond. Hence, it is important to investigate

the influence of bar diameter on the performance of strengthened beams. Figure 4.33

shows the effect of bar diameter on failure load in beams strengthened using the HSM

with CFRP. Data collected from beams H1BP8F16L80W1.2T and,

H1BP6F16L80W1.2T were used to analyze this influence. As shown in Figure 4.33, the

failure load increased with increasing bar diameter.

127

Figure 4.33: The effect of bar diameter

(c) Effect of Number of Bars or NSM Grooves

For every NSM bar used, a separate groove is required to place the bar in the concrete

beam. Thus, the number of bars is equal to the number of grooves. Figure 4.34 shows the

effect of number of grooves or bars on the performance of the HSM strengthened beams

with CFRP. The experimental data of H1B8F19L80W1.2T and H2B6F16L100W1.2T

were used to investigate this effect. It is important to note that the plate widths of the

plates are not the same and it cannot be compared directly. However, the harmful effect

of increased groove number can be easily understood. As shown in Figure 4.34, the

failure load decreased with increasing number of bars or grooves. Increasing the number

of grooves decreases both edge clearance and clear spacing between two adjacent

grooves. This increases the possibility of edge breakage. The beam specimens used in this

study may not have had enough width to place two bars with sufficient clearance.

Therefore, concrete separation may have been accelerated due to early edge breakage. A

similar effect was found in the study of Sharaky et al. (2014), where end slips for the two

beams each with two NSM bars were slightly higher than those of the beam with one

NSM bar, due to a lower confinement (edge effect) in the case of two NSM bars.

128

Figure 4.34: The effect of number of grooves on failure load

4.2.4 Eliminating End Debonding

4.2.4.1 Effect of Plate Thickness

Plate thickness is an important parameter for plate end debonding from concrete

substrate. The beam H1B8S19L73W1.5T, H1B8S19L73W2T and H2B6S19L73W2.76T

are used to observe this effect. According to Figure 4.35, the ultimate failure load

decreased with increasing thickness. An increase in thickness from 1.5 to 2.76 mm

resulted in, the failure load decreased from 137 kN to 130 kN. This happened due to

increased interfacial shear stress. Lousdad et al. (2010) found similar results.

129

Figure 4.35: The effect of plate thickness.

4.2.4.2 Effect of Shear Strengthening

Although the hybrid strengthening system improved the performance of strengthened

beams, it could not prevent premature debonding failure. Most of the HSM strengthened

beams failed in concrete cover separation. The cause of this failure mode was mostly

shear cracks and partly flexural shear cracks. To counter this, it was decided that the

internal shear capacity of a strengthened beam should be increased. In

H1B8SD19L73W2T, the spacing of the internal reinforcement was reduced to 40 mm

c/c. However, the failure load was decreased to 124 kN from 132 kN (H1B8S19L73W2T)

and the debonding failure mode could not be avoided. On the other hand, beam

H1B8S19L73W2TAS was strengthened in shear with externally bonded CFRP wrap. The

CFRP fabric was applied only to the side of the beam and not to the soffit. The failure

mode was interestingly changed to flexural failure. The failure load was increased to 135

kN, which was very close to the failure load of the end anchored beam,

H1B8S19L73W2TAF, which was fully wrapped with CFRP fabric.

130

4.2.4.3 Effect of End Anchorage

The effect of end anchorage was observed in H1B8F19L80W1.2TAF. CFRP wrap was

used in end anchorage at both ends. The failure load was increased to 164 kN without

premature debonding failure.

4.2.4.4 Effect of Location of the Steel Plate and Bar

The position of steel plate and bar influenced the failure mode of the HSM

strengthened RC beam. In beam SH2S61900L100W2T, the position of plate and bar was

changed from bottom to side (lower portion). The failure mode of the beam was changed

to flexural failure mode. However, the ultimate failure load of SH2S61900L100W2T

(HS12) decreased to 124 kN compared to H1B8S19L73W2T (HS1). This was attributed

to the reduction of the effective depth of the HSM strengthened composite beam.

4.2.5 Experimental Behaviour of Steel NSM Strengthened Beam

4.2.5.1 Load Carrying Capacity and Failure Mode

A summary of the flexural behaviour of all tested NSM strengthened beams in terms

of first crack load, yield load, flexural loading capacity and failure mode is shown in

Table 4.8. As shown in Table 4.8, the addition of steel bars as NSM reinforcement

increases the ultimate moment capacity by 22.5%, 46.8%, 43.75%, 26.46%, 23.26%,

32.8% and 25% for N2S6C, N2S6E, N2S6EC, N1S8E, N1S8C, N3S8C, N3S8C N1SH8C

and N2SS8C, respectively, as compared to the control beam. The yield capacity and the

first crack loads of the beams also increased after strengthening. The highest improvement

in ultimate load capacity was achieved in NS2, which increased by 46.8%. This is greater

than the increase in ultimate load capacity achieved by concrete beams strengthening with

NSM FRP in the studies done by Hassan and Rizkalla (2001) and Soliman (2008). Hassan

and Rizkalla (2001) found that NSM FRP strengthening increased the performance of the

RC beams by 39%, while Soliman (2008) found that such strengthening improved the

131

ultimate load capacity of the beams by 18%. As the cost of an FRP bar is twenty times

that of a steel bar (Hefferman, 1997), using NSM steel bars is a better option in terms of

both strengthening capacity and cost.

Table 4.8: First crack, yield and failure (and mode) of NSM beams

Beam no

First

crack load

(kN)

Increase in

first crack

load (%)

Bar

yield

load

(kN)

Failure

load

(kN)

Increase in

failure load

(%)

Mode of

failure

CB 12.5 - 72 80.0 - Flexural

failure

N2S6C 20.0 62.5 90 98.0 22.5 Flexural

failure

N2S6E 26.0 112.5 100 117.4 46.8 Flexural

failure

N2S6EC 22.0 79.1 92 115.0 43.8 Flexural

failure

N1S8E 28.0 129.1 100 101.2 26.5 Flexural

failure

N1S8C Pre-

cracked

- 90 98.0 23.3 Flexural

failure

N3S8C 25.0 104.1 100 106.2 32.8 Debonding

failure

N1SH8C 20.0 - - 135.0 - Flexural

failure

N2SS8C 20.0 62.5 - 100.6 25.0 Flexural

failure

The failure modes of the control beam and all the NSM strengthened beams are shown

in Figure 4.36 to Figure 4.44. The failure modes of the strengthened beams were found

to be very similar to each other, mostly by flexural failure. In flexural failure, concrete

crushing is followed by steel yielding. It is the most commonly reported mode of failure

in NSM strengthened structures. NSM strengthening is less prone to debonding.

However, the failure mode of the most heavily strengthened beam, N3S8C, was

premature debonding. An NSM steel bar separated from the concrete side face as shown

in Figure 4.42. Soliman et al. (2010) reported failure by concrete cover separation

observed in most of the beams tested in the study, which were strengthened using NSM

132

FRP bars. From this, it can be concluded that the bond performance of steel bars to

concrete is better than that of FRP bars to concrete.

Figure 4.36: Failure mode of control beam

Figure 4.37: Failure mode of N2S6C

133

Figure 4.38: Failure mode of N2S6E

Figure 4.39: Failure mode of N2S6EC

Figure 4.40: Failure mode of N1S8E

134

Figure 4.41: Failure mode of N1S8C

Figure 4.42: Failure mode of N3S8C

Figure 4.43: Failure mode of N1SH8C

135

Figure 4.44: Failure mode of N2SS8C

4.2.5.2 Effect of Strengthening on Deflection, Crack and Strain

Deflections (actuator) and reduction in deflections due to strengthening using NSM

steel bars were measured under 20 kN, 40 kN, and 60 kN service loads, as shown in Table

4.9. The deflections of the strengthened beams were reduced in comparison to the control

beam due to the increased stiffness of the strengthened beams.

136

Table 4.9: Reduction in deflection due to NSM strengthening

Beam

No.

Load at 20 kN Load at 40 kN Load at 60 kN

Deflection

in mm

(Instron)

Reduction

(%) over

CB

Deflection

in mm

(Instron)

Reduction

(%) over

CB

Deflection

in mm

(Instron)

Reduction

(%) over

CB

CB 2.42 - 5.51 - 8.48 -

N2S6C 1.48 39 3.71 33 5.01 41

N2S6E 1.55 36 3.23 41 5.26 38

N2S6EC 1.81 25 3.69 33 5.47 35

N1S8E 2.16 10 5.48 1 7.83 8

N1S8C 3.86 -* 5.17 6 6.81 20

N3S8C 1.39 43 3.12 43 6.94 18

N1SH8C 2.10 13 4.00 27 5.23 38

N2SS8C 2.04 16 4.20 24 6.44 24

* Deflection is more due to prior cracking.

The strain in the internal reinforcing steel bars and the reduction of strain in these bars

due to strengthening was measured at 20 kN, 40 kN, and 60 kN service loads as shown

in Table 4.10. The strain in the internal steel bars was significantly reduced in the

strengthened beams. Thus, according to Hooke’s law, the stress in the rebars was likewise

reduced. Due to the reduction in stress, the fatigue life of the strengthened beam should

also have increased according to the S-N curve relation for steel bars (Helagson &

Hanson, 1974; Moss, 1982).

137

Table 4.10: Reduction of strain in steel rebars due to NSM strengthening

Beam

No.

Load at 20 kN Load at 40 kN Load at 60 kN

Bar

Strain

Reduction

(%)

Bar

Strain

Reduction

(%)

Bar

Strain

Reduction

(%)

CB 793 - 1661 - 2507 -

N2S6C 556 30 1059 36 1509 40

N2S6EC 248 69 1465 12 3006 20

N1S8E 406 49 1528 8 2418 4

N3S8C -* - 933 44 1523 39

N1SH8C 319 60 737 56 1451 51

*The value was missing due to delay in interval setting.

The strain in the concrete at the surface of the beams and the reduction of these

concrete strains due to strengthening were measured at 20 kN, 40 kN, and 60 kN service

loads, as shown in Table 4.11. The concrete strain was reduced significantly in the

strengthened beams.

Table 4.11: Reduction in concrete strain due to NSM strengthening

Beam

No.

Load at 20 kN Load at 40 kN Load at 60 kN

Concrete

strain

Reduction

(%)

Concrete

strain

Reduction

(%)

Concrete

strain

Reduction

(%)

CB 252 - 602 - 990 -

N2S6C 175 31 376 38 510 48

N2S6E 126 50 337 44 542 45

N1S8C 200 21 383 36 550 44

N3S8C -* - 450 25 697 30

N1SH8C 215 15 408 32 609 38

*The value was missing due to delay in interval setting.

4.2.5.3 Effect of Different Parameters

Strengthening with different configurations was investigated to identify the most

suitable arrangement to achieve the best improvement in flexural performance of the RC

beam strengthened with steel bars.

138

(a) Effect of Adhesive Type

The effect of adhesive type on the performance of the NSM strengthened RC beam is

shown in Figure 4.45. Based on experimental data of N2S6C and N2S6E, as the adhesive

type changed from cement mortar to epoxy, the failure load increased from 98 kN to

117.44 kN. This is normal behaviour because bonding strength of epoxy is significantly

higher than that of cement mortar. First crack load also increased from 20 kN to 26 kN

due to change of adhesive type. The load deflection behaviour of CB, N2S6C and N2S6E

is shown in Figure 4.46.

Figure 4.45: The effect of adhesive type on first crack and failure load

139

Figure 4.46: Load-deflection diagram of CB, N2S6C and N2S6E

(b) Effect of Partial Epoxy Replacement with Cement Mortar

Cement mortar has inferior mechanical properties and durability, with a tensile

strength lower than that of commercially available epoxies (De Lorenzis & Teng, 2007).

Results of bond tests and flexural tests (Nordin & Taljsten, 2003; Taljsten et al., 2003)

have identified some significant limitations of cement mortar as a groove filler. However,

bond stresses are not equally distributed along the length of an NSM bar, as shown in

Figure 4.47. Maximum bond stresses are found near the ends of the NSM bar and they

gradually decrease towards the mid span of the beam. This characteristic variation of bond

stresses may allow the partial replacement of epoxy with cement mortar.

140

Figure 4.47: Bond stresses in the longitudinal plane (De Lorenzis & Teng, 2007)

Since the bond stresses at the midsection of a beam are relatively low, the NSM

grooves could be filled with cement mortar at this location. However, in other places,

particularly at the groove end, the groove should be filled with epoxy adhesive due to the

presence of higher bond stresses. The effect of the partial replacement of epoxy with

cement mortar is shown in Figure 4.48. The failure load of N2S6EC (50% epoxy replaced

with cement mortar) is almost similar to the failure load of N2S6E (epoxy used entirely)

but significantly higher than that of N2S6C (where cement mortar is used entirely).

However, the stiffness of N2S6EC is slightly lower than that of N2S6E because the

deflection of beam N2S6EC is lower than the deflection of N2S6E due to presence of

cement mortar as shown in the load-deflection diagram of Figure 4.49 (LVDT data are

used). This is due to the presence of cement mortar.

141

Figure 4.48: The effect of partial replacement of epoxy with cement mortar

Figure 4.49: Load-deflection diagram of CB, N2S6E and N2S6EC

(c) Effect of Number of NSM Grooves

Each NSM bar used to strengthen a concrete beam requires a groove to be placed in.

Thus, the number of grooves is equal to number of bars used. The experimental data of

specimens N2S6C and N1S8C were used to investigate the effect of number of grooves

on the performance of beams where cement mortar was used in strengthening. Data from

98

117.44115

85

90

95

100

105

110

115

120

Ult

imate

Load

( k

N)

Bonding Materials

Ultimate Load (kN)

142

specimens N2S6E and N1S8E were used to investigate this effect on beams that used

epoxy adhesive. However, the total amount of strengthening reinforcement in both cases

was similar (56 mm). Figure 4.50 shows the effect of number of grooves on the

performance of beams strengthened using the NSM technique, with the same amount of

reinforcement, but different adhesives.

Figure 4.50: The effect of number of grooves

As can be seen from Figure 4.50, the failure load increased when the number of

grooves was increased from one to two in the case of beams using epoxy adhesive.

However, in the case of the beams using cement mortar, the failure load was almost the

same. The increase in groove number provides an additional amount of groove fillers in

concrete beam. The load-deflection diagram of CB, N2S6C, N2S6E, N1S8E, N1S8C are

shown in Figure 4.51 and Figure 4.52

0

20

40

60

80

100

120

140

One Two

Ult

ima

te L

oa

d (

kN

)

Number of Grooves

Cement

Epoxy

143

Figure 4.51: Load-deflection of CB, N2S6C and N1S8C with cement mortar

Figure 4.52: Load-deflection diagram of CB, N2S6E and N1S8E

(d) Effect of Bar Numbers with the Same Diameter

The effect of bar number is shown in Figure 4.53. The amount of reinforcement used

is the single most important parameter in the flexural strengthening of RC beams.

Increasing the number of NSM bars provides additional reinforcement to the concrete

144

beam, but decreases both edge clearance and the clear spacing between two adjacent

grooves. This increases the possibility of the edge of the beam breaking off. The width of

the beam specimens used in this study was not sufficient to place two or three 8 mm bars

on the bottom face of the beam according to ACI 440. Thus, in specimen N3S8C, which

used three 8 mm bars, the bars were placed at different positions (one at the bottom and

two at opposite sides and in N2SS8, which used two 8 mm bars, the bars were placed at

opposite sides of the beam

Figure 4.53: The effect of bar number on the performance of NSM beam

Figure 4.53 shows the effect of number of bars on failure behaviour of the RC beam

strengthened with NSM steel bar using cement mortar as adhesive. Beams N1S8C,

N3S8C and N2SS8C are used to observe this effect. The load deflection diagram of CB,

N1S8C and N3S8C is shown in Figure 4.54. Failure modes were changed in N3S8C from

flexural failure to debonding failure.

98

99

100

101

102

103

104

105

106

107

0 1 2 3 4

Failu

re lo

ad(k

N)

Number of bars

The effect of no. of bars

The effect of no. ofbars

145

Figure 4.54: Load-deflection diagram of CB, N1S8C and N3S8C

(e) Effect of Internal Reinforcement

In beam N1SH8C, a higher internal reinforcement was used. Instead of bar diameter

of 12 mm, two 16 mm bars were used as internal reinforcement. This caused the failure

load to increase to 135 kN. However, the failure mode remained the same, i.e. flexural

failure (concrete crushing followed by steel yielding).

4.2.5.4 Comparison of NSM with EBR

Compared to externally bonded reinforcement, the NSM system has several

advantages. Figure 4.55 compares the performance of NSM strengthening and EBR

strengthening.

146

Figure 4.55: Comparison of NSM with EBR

4.2.6 Fatigue Performance of the HSM Strengthened Beam

4.2.6.1 Failure Mode

Two modes of failure were observed for the cyclically loaded RC beams. Fatigue

failure in the tension steel reinforcement was the usual mode of failure. This mode of

failure was expected as the stress range in the tension steel reinforcement was high

enough to cause fatigue failure in the steel. The control beams, CBF1, CBF2 and the NSM

strengthened beam, NSF, failed in this mode of failure. Figure 4.56 and Figure 4.57 shows

the fatigue failure mode of CBF1. Figure 4.58 shows the failure mode of NSF. The EBR

beam and the HSM strengthened beam (with steel bar and steel plate) both failed in

debonding failure, as shown in Figure 4.59 and Figure 4.60.

147

Figure 4.56: Fatigue failure mode of control beam

Figure 4.57: Fatigue fracture of steel

Figure 4.58: Failure mode of NSF

148

Figure 4.59: Failure mode of PSF

Figure 4.60: Failure mode of HSF

4.2.6.2 Number of Cycles to Failure

Table 4.12 shows the number of cycles to failure of the beams tested under fatigue

loading. The fatigue life of the strengthened beams increased. The fatigue testing of PSF

ceased after 2x106 cycles. PSF and HSF were loaded monotonically to failure. The fatigue

life of the strengthened beams increased after strengthening due to the redistribution of

stresses between the internal reinforcement and the external reinforcement, resulting in

lower stresses in the internal steel reinforcement.

149

Table 4.12: Result of fatigue test

Sl.

No.

Beam Minimum

Load

(kN)

Maximum

Load (kN)

Number of

cycles to

failure

Post

fatigue

load (kN)

Failure mode

1 CBF1 10 40 (.5fy) 485000 - Fracture of

steel

2 CBF2 10 64 (.8fy) 188000 - Fracture of

steel

3 NSF 10 64 (.8fy) 198000 - Fracture of

steel

4 PSF 10 64 (.8fy) >2000000 98.00 Debonding

5 HSF 10 64 (.8fy) 211000* 136.34 Debonding

*After this cycle the load of the Instron machine accidentally increased from 64 to 136.34

kN due to some error (tripped) and fatigue testing could not be continued.

4.3 Verification of Semi-numerical Model

4.3.1 Verification of Flexural Strength Model

To verify the flexural strength model, the ultimate failure loads of the control beam

and beam H1B8S19L73W2TAF were evaluated. The correlation between the

experimental and the predicted results for these beams is within a reasonable range of

agreement. Figure 4.61 shows the predicted and experimental failure loads.

Figure 4.61: Predicted and experimental failure load

150

4.3.2 Verification of Deflection Prediction Model

To verify the deflection prediction model, the measured load versus deflection

relationships at mid-span during loading were compared with the analytical results

obtained from the model. Figure 4.62 and Figure 4.63 show the predicted and the

experimental deflection measurements of the control beam, CB, and H1B8S19L73W2T

(HSM with steel plate and steel bar) at different service loads.

Figure 4.62: Predicted and experimental load-deflection diagram of CB

Figure 4.63: Predicted and experimental load-deflection of H1B8S19L73W2T

151

4.3.3 Verification of Debonding Strength Model

To verify the debonding strength models, debonding failure loads of PS19L73W2.76T

(PS1), PS16L73W2.76T (PS2), H1B8S19L73W2T (HS1) and H1B8S16L73W2T(HS2)

were evaluated. In addition, beams A3, A5, SM4, SM5, and B2 were taken from the

previous studies (Arduini et al., 1997, Arduini and Nanni, 1997, Quantrill et al., 1996).

These beams were evaluated using the proposed debonding strength model. The

correlation between the experimental and predicted results for the test beams is within

reasonable agreement for both EBR and HSM strengthened beam. Figure 4.64 shows the

predicted and experimental measurements of load.

Figure 4.64: Predicted and experimental debonding failure load

4.3.4 Parametric Study using Debonding Strength Model

The effect of steel plate thickness and length using the debonding strength model is

shown in Figure 4.65 and Figure 4.66. According to Figure 4.65, debonding failure load

decreased with plate thickness and this trend is also similar to the experimental trend.

0

20

40

60

80

100

120

140

160

180

PS1 PS2 HS1 HS2 A3 A5 SM4 SM5 B2

De

bo

nd

ing

Failu

re lo

ad(k

N)

Beam

Experimental

Model

152

Figure 4.65: The effect of plate thickness using the debonding strength

model

Figure 4.66: The effect of plate length using the debonding strength model

153

4.4 Finite Element Numerical Results

The numerical and experimental results in the following sections are presented in terms

of the ultimate load carrying capacities, and deformational characteristics of the beams

when using the presented model. The meshing with deflected shape of quarter of typical

beam is shown in Figure 4.67 (3D).

Figure 4.67: Meshing with deflected shape

4.4.1 Load Carrying Capacities

The comparison between finite element numerical and experimental results for the

steel HSM strengthened beam specimens in terms of load at first crack, yield load and

ultimate load is summarized in Table 4.13. As shown in Table 4.13, there is a good

agreement between the predicted load carrying capacities and the experiment result of

most of the test specimens.

154

Table 4.13: The comparison between numerical and experimental results

Beam Id Load at first

crack

(kN)

Yield load

(kN)

Ultimate load

(kN)

Ratio

Num. Exp. Num. Exp. Num. Exp. Num./exp.

CB 16 12.5 74 72 82 80.0 -

H1B8S19L73W2T 38 40.0 - - 132 132.0 1.05

H1B8S16L73W2T 35 58.0 85 82 110 106.0 1.03

H1B6S16L73W2T 35 60.0 80 80 98 102.0 0.97

H2B8S19L73W2T 30 48.0 - - 105 109.0 0.97

H2B6S19L73W2T 35 30.0 - - 108 110.0 0.98

H2B6S19L73W2.76T 60 40.0 120 122 132 130.0 1.02

H2B6S19L125W1.5T 35 53.0 125 128 138 135.0 1.02

H1B8S19L73W2TAS 30 40.0 127 126 138 137.0 1.03

H1B8S19L73W2TAF 30 40.0 110 115 138 137.3 1.03

SH2S61900L100W2T 35 60.0 112 116 126 123.0 1.02

Two types of failure mode have been observed. The flexural failure modes were

observed in control and NSM strengthened beams as shown in Figure 4.68 and Figure

4.69 and debonding failure modes in the form of concrete cover separation were observed

in most of the HSM strengthened beams as shown in Figure 4.70 (Full scale).

155

Figure 4.68: Typical flexure failure mode of control beams (2D)

Figure 4.69: Typical flexure failure mode of NSM strengthened beams (2D)

Figure 4.70: Typical debonding failure mode of HSM strengthened beam (2D)

156

4.4.2 Load-Deflection Relationship

The validity of the model to simulate the behaviour of RC beams strengthened using

HSM was examined by comparing the experimental test results presented in Chapter 4.

Figure 4.71, Figure 4.72 and Figure 4.73 show the load-deflection curves for the control

specimen, the typical steel NSM and HSM strengthened beam specimens, respectively.

The dotted and firm lines represents the curve of experimental and numerical results

respectively. It can be observed that the correlation is reasonably good between the

numerical result and the experimental data.

Figure 4.71 : Load deflection diagram of control beam

157

Figure 4.72 : Typical Load deflection diagram of NSM strengthened beam

Figure 4.73: Typical Load deflection diagram of HSM strengthened beam

158

During the first stage, the displacement increases almost linearly with the load, the

slopes of the curves are similar and Young's modulus has its greatest value. In the second

stage, the cracks propagate and steel bars take the traction and there is noticeable non-

linearity and irreversibility in beam property. Furthermore, the displacement increases

faster than load which means a drop in Young's modulus. In other words, a reduction in

the beam stiffness occurs.

To increase the bending resistance of the reinforced concrete beams, the steel or FRP

plate is attached to the bottom of the beams in this section. The thickness of each FRP

layer is 1.2 mm. The predicted ultimate load of 82 kN is in reasonable agreement with the

experimental ultimate load 80 kN. Hence, the material constitutive models have been

proven to be able to simulate the composite behaviour of reinforced concrete beams

strengthened by FRP correctly.

4.4.3 Parametric Study using Finite Element Modelling

The effect of FRP plate thickness and length using finite element analysis is shown in

Figure 4.74 and Figure 4.75. According to Figure 4.74, debonding failure load decreased

with plate thickness and this trend is also similar to the experimental trend.

159

Figure 4.74: The effect of plate thickness using FEA

Figure 4.75: The effect of plate length using FEA

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5

Lo

ad

(in

kN

)

Plate Thickness (in mm)

The effect of platethickness

0

20

40

60

80

100

120

140

160

180

200

1600 1650 1700 1750 1800 1850 1900 1950

Load

(in

kN

)

Plate Length (in mm)

The effect of Plate length

160

The ultimate load increased with plate length according to Figure 4.75, and this trend

is also similar to the experimental observation and the trend in published literature. The

findings of this investigation will be of interest to researchers and engineers looking to

apply FRP composites in civil engineering applications, and may provide some

implications for future design codes. All strengthened beams exhibited a higher load

capacity and a lower ductility compared with their respective control beams. The non-

linear three-dimensional finite element model proposed herein provides researchers and

designers a computational tool for the design of FRP strengthened beams. Through FEA

modelling, the reduction in deflection and the maximum improvement in strength due to

different configurations of FRP can be obtained. With the proposed FEA modelling, it is

possible to do trial and error to find an effective and reasonable retrofit scheme.

4.5 Solution of Mathematical Optimization

4.5.1 Non-linear Programming Solutions

The present study considers an example of optimization done by Arya et al. (2002).

This study optimized the flexural strengthening (using CFRP) of a simply supported 9 m

span RC beam. The beam was designed with a 350 mm wide (b) and 700 mm deep (h)

concrete section and with 2532 mm2 internal reinforcement to support characteristic dead

(ginitial) and imposed loads (qinitial) of 15 kN/m and 21 kN/m, respectively. The beam was

then strengthened to carry additional dead (gad) and imposed loads (qad) of 5 kN/m and 7

kN/m respectively. To achieve this, an externally bonded CFRP plate was attached to

soffit of the beam. The common data used in this example are presented in Table 4.14.

161

Table 4.14 : The common data used for calculation

Materials properties and partial safety factors

Concrete Steel

reinforcement

CFRP

fcu 40 MPa fy 460 MPa ffk 2500 MPa

Ec 31MPa Es 200 GPa Efk 65 GPa

εcu 0.0035 εy 0.002 εfk 0.013

γmc 1.5 γms 1.15 γmf 1.4

γmm 1.1

The problem in this example was solved using the non-linear programming approach

used in the present research with previously mentioned parameters. From the analysis the

optimum dimensions for the CFRP plate are given in Table 4.15 and 7.18 m length. The

cost of this option (RM 5333) is RM 451 less than the option (RM 5785) made by Ayra

et al. (2002). Thus, the cost savings of the proposed optimization method would be 8.5%

over the previous optimization model of Arya et al. (2002).

Table 4.15 : Result of FRP strengthening using non-linear programming

Design variable Optimum value of

continuous variables

Tradition value

of the variable

Plate width, b (mm) 214.6 240.0

Plate height, h (mm) 1.44 1.40

Length of FRP plate (mm) 7180 7160

Total cost(RM) 5333 5785

Saving in cost 8.5% 0%

4.5.2 Genetic Algorithm Solutions

Applying genetic algorithms to the example problem from Arya et al. (2002) was

solved using the previously mentioned parameters. The optimum dimensions for the

CFRP plate are given Table 4.16 and corresponding length of 7.18 m. The cost of this

option (RM 5357) is RM 428 less than the option (RM 5785) made by Ayra et al. (2002).

162

The cost savings made from using the proposed genetic algorithms for optimization

would be 8%. As the example from Arya et al. was taken from an academic journal that

has been evaluated by a number of reviewers, the cost savings made from this

optimization method using genetic algorithms would probably be even greater in the

professional or practical field.

Table 4.16 : Result of FRP strengthening using the genetic algorithm

Design variable Optimum value of

continuous variables

Tradition value

of the variable

Plate width, b (mm) 217 240

Plate height, h (mm) 1.42 1.40

Length of FRP plate (mm) 7180 7160

Total cost(RM) 5357.00 5785.00

Saving in cost 8.0% 0%

Regarding the technical performance criteria of the optimized plate dimensions, the

resistance bending moment capacity of the optimized plate is equal to 737.31 kN-m which

is slightly greater than the external moment (733.71 kN-m). The calculated longitudinal

shear stress is equal to 0.78 N/mm2 which is less than the allowable limit (0.8N/mm2) set

against premature separation failure. In terms of serviceability, the estimated concrete

stress (18.54 N/mm2) and steel stress (319 N/mm2) are significantly less than the

allowable limits (24 N/mm2 for concrete and 368 N/mm2 for steel).

An important finding in this research is that if the cost of adhesive and surface

preparation is ignored, the optimum dimensions of the CFRP plate is 256 mm wide and

1.21 mm deep with a corresponding length of 6.88 m long. It has been demonstrated that

163

the cost of the strengthening materials is an important consideration in any structural

design process. This optimization procedure based on genetic algorithms can be an

effective tool to make the design process more efficient and therefore lead to the proper

and efficient use of structural strengthening materials.

4.6 Summary of the Results and Discussion

This section demonstrates how the results of this chapter are used to achieve the

objective of this study. Most of objectives were successfully achieved through

experimental investigation, analytical study, finite element modelling and mathematical

optimization, as revealed in Table 4.17.

Since the cost of the steel bar and cement mortar is significantly lower than that of

FRP bar and epoxy adhesive, the use of these material certainly reduces the cost of

strengthening. On the other hand, the application of HSM increases the performance.

Both reduction of cost and enhancement of performance help to achieve the goal of the

research, i.e increase the efficiency of the structural strengthening system. Mathematical

optimization further increases the efficiency by reducing the cost of the material.

Therefore, the current goal of this study has been successfully achieved.

164

Table 4.17: Achievement of Objectives

Sl. No. Objectives Beam How to achieve

1

Develop a strategy for eliminating premature

failures of strengthened beams using hybrid

strengthening method (HSM).

Beam Sl. No

10-15, 21-27 (13beams)

Effectiveness: The ultimate load capacity of all hybrid strengthened beam

increased by 26%-72% respectively, compared to the control beam

Efficiency: The ultimate load capacity of all hybrid strengthened beam

increased by 6%-36% respectively, compared to the RC beam strengthened

with EBR Beam Sl. No

10,11,21,22 (4 Beam)

Compare to PS1, PS2, PF1,

PF2

Beam Sl. No. 16

17

20, 26

19

28(6 beams)

i) Increase of internal shear strength: Not eliminated

ii) Increase of plate width: Not eliminated

iii) Use of End Anchor: Eliminated

iv) Increase of external shear strength: Eliminated

v) Use of side hybrid bond: Eliminated

2 Study the effectiveness of using cement mortar to

replace epoxy and steel bar to replace FRP in NSM

strengthening method.

Beam Sl. No

2-9 (8beams)

The ultimate load capacity of all NSM strengthened beam increased by 22.5%-

46.8% respectively, compared to the control beam

3 investigate the fatigue performance of RC beams

strengthened with HBR, EBR, and NSM

Beam Sl. No.

30-34 (5 beams)

Fatigue performance of strengthened beams are used to achieve this objective.

5

Develop a semi-numerical and finite element model

(FEM) to predict flexural strength and deflection of

RC beams strengthened using the HSM.

Beam Sl. No

10,11 (2 Beams)

The correlation between the experimental and predicted results from semi

numerical mode is within a reasonable agreement that support objective four

Beam Sl. No

10-28

The correlation between the experimental and predicted results from finite

element model is within a reasonable agreement that support objective

7 Propose an economical approach for flexural

strengthening of RC beams with CFRP plate based on

non-linear and genetic algorithm.

Significant cost savings from optimization task of the efficient design method

proved the achievement.

165

CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusions

The study presents the results of the research under in developing a strategy for

eliminating premature failure of strengthened RC beams, which was called HSM and in

proposed in the study. This technique was shown to have helped in reducing the

possibility of premature failure and more efficient compared to the existing strengthening

techniques. In the study of replacing epoxy by cement mortar and FRP by steel bar

promising results were also obtained. The fatigue performance of the hybrid strengthened

RC beams were shown to be better than the other techniques. Semi-numerical and finite

element models were developed to predict the flexural strength and deflection of RC

beams strengthened with different techniques. Developed an easy, efficient, and direct

closed-form solution model for optimization of design of steel and FRP strengthened RC

beams using non-linear and genetic algorithms. Based on study carried out, the following

conclusions can be drawn:

i. Experimental result shows that strengthening with the HSM has been proven to

be an effective alternative to the current strengthening techniques under

monotonic and fatigue loadings.

ii. The load carrying capacity of the HSM strengthened RC beam specimens

increased by up to 65% for RC beam strengthened with steel plate and steel bar

and 104% for RC beam strengthened with CFRP plate and steel bar.

iii. The performance to increase load carrying capacity of the HSM strengthened

beam to increase load carrying capacity was up to 36% higher than the

corresponding EBR when the same amount of strengthening materials were used.

iv. The performance of the bond between the concrete and the plate improved by 25%

in the hybrid strengthening technique, even for the same plate thickness.

166

Separation or delamination of CFRP or steel plate from concrete substrate was

successfully prevented due to this improved bond performance.

v. The number of grooves adversely affected the performance of the HSM because

of availability of sufficient beam width for providing enough space to make the

grooves. Similarly, the effect of diameter of NSM bar on the strengthening

performance of HSM beams is considerable.

vi. The ductility of the HSM strengthened beams was found to be very similar to that

of the un-strengthened control beams. Interestingly, the energy absorption

capacity the HSM strengthened beams was significantly higher than that of the

un-strengthened control beams due to higher ultimate and failure load.

vii. The premature failure, i.e. delamination or concrete cover separation of HSM

strengthened beams were successfully eliminated through decreasing the plate

thickness, proper external shear strengthening, especially in cases of concrete

cover separation, providing traditional end anchorage using CFRP wrapping, and

changing the location of the bars and plates from soffit to sides.

viii. Using NSM steel bars to strengthen RC beams is an economical alternative to

strengthening with NSM FRP bars. The beams where 50% of the epoxy adhesive

was replaced with cement mortar in the middle part of the NSM groove gave

flexural performances almost similar to the performances of the beams using

100% epoxy adhesive.

ix. The fatigue performance of the HSM strengthened beam was found to be higher

than that of the NSM strengthened beam. In addition, the fatigue failure of the

HSM strengthened beam was not found to be brittle or sudden compared with the

NSM strengthened beam.

x. The proposed semi-numerical model was shown to be an alternative

computational method to the trial and error procedure for the design of an effective

167

and reasonable retrofit scheme. The results of the finite element models were

found to be consistent with the experimental test results.

xi. The non-linear programming and genetic algorithms provided a procedure that

can be applied to produce economical solutions when designing FRP

strengthening systems and this design process may lead to significant savings in

the quantity of strengthening materials to be used in comparison to traditional

design methods.

5.2 Recommendations

The present study illustrates the hybrid strengthening method (HSM) for strengthening

RC beams and its practical suitability. HSM has huge potential for applications in

structural strengthening. The following important recommendations are to be considered

for future work in this area:

i. The structural performance of RC beams flexurally strengthened with

prestressed HSM using steel and FRP should be explored.

ii. The flexural performance of prestressed beams strengthened with HSM

using FRP and steel reinforcement should be studied.

iii. The flexural behaviour of pre-cracked beams strengthened with HSM

should also be investigated for their performance.

iv. The fatigue performance of RC or prestressed beams strengthened with

HSM using FRP or steel reinforcement should be tested.

v. In this research, cement mortar used to replace 50% of epoxy adhesive.

Future investigations are required to investigate the different percentages of

replacement of epoxy adhesive by cement mortar.

vi. Design guidelines need to be developed for the practical application of

HSM.

168

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TEST RESULTS FOR CONCRETE AND STEEL PROPERTIES

A.1 Concrete Properties

Table B1: Concrete strength of the beam specimens

No. Series Notation

Average

Compressive

Strength

(MPa)

Average

Flexural strength

(MPa)

1 C Series

(Figure 3.13)

CB

34.3 3.8

2

N Series

(Figure 3.15)

N2S6C 40.9 4.3

3 N2S6E 40.6 3.9

4 N2S6EC 25.9 3.6

5 N1S8E 29.2 3.5

6 N1S8C 20.1 3.5

7 N3S8C 20.1 3.2

8 N1SH8C 34.5 3.4

9 N2SS8C 26.8 4.0

10

H Series

(Figure 3.16)

H1B8S19L73W2T 27.1 3.4

11 H1B8S16L73W2T 35.3 3.4

12 H1B6S16L73W2T 36.1 3.4

13 H2B8S19L73W2T 38.0 3.4

14 H2B6S19L73W2T 35.8 4.3

15 H2B6S19L73W2.76T 26.7 3.9

16 H2B6S19L125W2T 29.8 4.3

17 H1B8SD19L73W2T 21.2 3.7

18 H2B6S19L125W1.5T 21.7 3.3

19 H1B8S19L73W2TAS 31.3 3.4

20 H1B8S19L73W2TAF 21.7 3.5

21 H1B8F19L80W1.2T 35.0 4.0

22 H1B8F16L80W1.2T 28.2 4.3

23 H1BP8F16L80W1.2T 30.2 4.0

24 H1BP6F16L80W1.2T 32.6 4.2

25 H2BP6F16L80W1.2T 33.8 4.4

26 H1B8F19L80W1.2TAF 22.5 3.5

27 H1B6FR19L100W.17T 29.5 3.4

28 SH Series

(Figure 3.17)

SH2S61900L100W2T

27.8 3.6

29

Fatigue

Series

CBF50 26.8 3.8

30 CBF80 39.8 4.0

31 PSF 37.6 4.0

32 NSF 34.5 4.0

33 HSF 21.7 3.1

184

A.2 Steel Properties

Figure A1: The result of tensile test of 6 mm bar

185

A.3 Equipment Used in Experiment

(a)

(b)

Figure A2: Testing of concrete for compressive strength (a) and flexural strength (b).

186

Figure A3: Data logger TDS-530

Figure A4: Digital Demec reader

187

NECESSARY CALCULATIONS

B.4 Moment capacity of control beam

The moment capacity of the control beam has been calculated according to EC2. Load

capacity was calculated from the moment capacity.

(B.1)

where:

α=0.85

Fck=30 Mpa

x= depth of neutral axix

b = 125 mm

(B.2)

Where

As= 226 mm

fy=580 Mpa

188

(B.3)

Where :

εs= Steel Strain

εult= Ultimate Strain of Concrete

Fc =

Fs=

Thus x=44.7 mm

Εult=0.0035 (Assumed)

Hence εs= 0.0076 >0.002

So reinforcement has yielded

Mult=Fs(d-0.44x) (B.4)

=22.24 kN-m

P= (B.5)

=68.43 kN

189

B.5 Shear Capacity of Control beam

Vcap=Vc+Vs (B.6)

Where

Vc= (B.7)

=13.94 kN

Vs= (B.8)

=45.57 kN

Vcap=13.94+45.57=59.5 kN

B.6 Sample Calculation for Debonding Strength Model

b = 200 mm; h = 200 mm; As = 308 mm2; d = 163 mm; As’= 308 mm2; dc = 37 mm; bf

= 150 mm; Ef = 167,000 MPa; Lf= 150 mm; L = 2000 mm; tf = 2.6 mm; Ea = 11,000 MPa;

ta= 1.0 mm; fc’= 33 MPa; and

Pu = 90 kN (experimental).

(B.9)

(B.10)

(B.11)

190

(B.12)

(B.13)

(B.14)

(B.15)

(B.16)

(B.17)

(B.18)

(B.19)

(B.20)

Interfacial shear stress,

191

(B.21)

(B.22)

Maximum interfacial shear stress at plate curtailment

(B.23)

(B.24)

Now the principle stress

(B.25)

So the predicted load is 92 kN

192

EXPERIMENTAL AND NUMERICAL LOAD DEFLECTION CURVES

Figure C 1: Load-deflection diagram of N2S6C

193

Figure C 2: Load-deflection diagram of N2S6E

Figure C 3: Load-deflection diagram of N2S6EC

194

Figure C 4: Load-deflection diagram of N1S8E

Figure C 5: Load-deflection diagram of N3S8C

195

Figure C 6: Load-deflection diagram of N1SH8C

196

Figure C 7: Load-deflection diagram of H1B8S19L73W2T

Figure C 8: Load-deflection diagram of H1B8S16L73W2T

Figure C 9: Load-deflection diagram of H1B6S16L73W2T

197

Figure C 10: Load-deflection diagram of H2B8S19L73W2T

Figure C 11: Load-deflection diagram of H2B6S19L73W2T

198

Figure C 12: Load-deflection diagram of H2B6S19L73W2.76T

Figure C 13: Load-deflection diagram of H2B6S19L125W1.5T

199

Figure C 14: Load-deflection diagram of H1B8S19L73W2TAS

Figure C 15: Load-deflection diagram of H1B8S19L73W2TAF

200

Figure C 16: Load-deflection diagram of SH2S61900L100W2T(HS12)

Figure C 17: Load-deflection diagram of H1B8F19L80W1.2T

201

Figure C 18: Load-deflection diagram of H1B8F16L80W1.2T

Figure C 19: Load-deflection diagram of H1BP8F16L80W1.2T

202

Figure C 20: Load-deflection diagram of H1BP6F16L80W1.2T

Figure C 21: Load-deflection diagram of H1B8F19L80W1.2TAF

203

Figure C 22: Load-deflection diagram of H1B6FR19L100W.17T

204

LIST OF PUBLICATIONS AND PAPERS PRESENTED

i. Moshiur Rahman , Mohd Zamin Jumaat, Muhammad Ashiqur Rahman,

Ismail M. I. Qeshta1 (2015), “Innovative HSM for Strengthening RC Beam

in Flexural” published in Construction and Building Materials Journal.

ii. Md. Moshiur Rahman , Mohd Zamin Jumaat, Md. Akter Hosen, A. B. M

Saiful Islam (2015), “The effect of Replacement of Adhesive with Cement

Mortar on the Performance of RC Beam with Near Surface Mounted Steel

Bar” Accepted for publication in Accepted for publication in Revista de la

Construcción. In press, corrected Proof.

iii. Md. Moshiur Rahman , Mohd Zamin Jumaat, Md. Akter Hosen(2012),

“Genetic Algorithm for Material Cost Minimization of External

Strengthening System with Fiber Reinforced Polymer” Accepted for

publication in Advanced Materials Research Journal.

iv. Md. Moshiur Rahman , Mohd Zamin Jumaat,(2012) “Cost Minimum

Proportioning of NonSlump Concrete Mix using Genetic Algorithms”

Accepted for publication in Advanced Materials Research Journal.

v. Md. Safiuddin, Ubagaram Johnson Alengaram, Md. Moshiur Rahman,

Md. Abdus Salam, and Mohd Zamin Jumaat,(2012) “Use of Recycled

Aggregate in Concrete : Accepted for publication in Journal of Civil

Engineering and Management.

vi. Md. Safiuddin, Mohd Hafizan Md.Isa, Md. Moshiur Rahman, Md. Abdus

Salam, Mohd Zamin Jumaat,(2012)“ Properties of self-consolidating POFA

Concrete” Accepted for publication in Advanced Science Letter.